diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -10770,18 +10770,49 @@
     return false;
   }
 
-  // Unsigned comparison is the same as signed comparison when both the operands
-  // are non-negative or negative.
   auto IsSignFlippedPredicate = [](CmpInst::Predicate P1,
                                    CmpInst::Predicate P2) {
     assert(P1 != P2 && "Handled earlier!");
     return CmpInst::isRelational(P2) &&
            P1 == CmpInst::getFlippedSignednessPredicate(P2);
   };
-  if (IsSignFlippedPredicate(Pred, FoundPred) &&
-      ((isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) ||
-       (isKnownNegative(FoundLHS) && isKnownNegative(FoundRHS))))
-    return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);
+  if (IsSignFlippedPredicate(Pred, FoundPred)) {
+    // Unsigned comparison is the same as signed comparison when both the
+    // operands are non-negative or negative.
+    if ((isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) ||
+        (isKnownNegative(FoundLHS) && isKnownNegative(FoundRHS)))
+      return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, CtxI);
+    // Create local copies that we can freely swap and canonicalize our
+    // conditions to "le/lt".
+    ICmpInst::Predicate CanonicalPred = Pred, CanonicalFoundPred = FoundPred;
+    const SCEV *CanonicalLHS = LHS, *CanonicalRHS = RHS,
+               *CanonicalFoundLHS = FoundLHS, *CanonicalFoundRHS = FoundRHS;
+    if (ICmpInst::isGT(CanonicalPred) || ICmpInst::isGE(CanonicalPred)) {
+      CanonicalPred = ICmpInst::getSwappedPredicate(CanonicalPred);
+      CanonicalFoundPred = ICmpInst::getSwappedPredicate(CanonicalFoundPred);
+      std::swap(CanonicalLHS, CanonicalRHS);
+      std::swap(CanonicalFoundLHS, CanonicalFoundRHS);
+    }
+    assert((ICmpInst::isLT(CanonicalPred) || ICmpInst::isLE(CanonicalPred)) &&
+           "Must be!");
+    assert((ICmpInst::isLT(CanonicalFoundPred) ||
+            ICmpInst::isLE(CanonicalFoundPred)) &&
+           "Must be!");
+    if (ICmpInst::isSigned(CanonicalPred) && isKnownNonNegative(CanonicalRHS))
+      // Use implication:
+      // x <u y && y >=s 0 --> x <s y.
+      // If we can prove the left part, the right part is also proven.
+      return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
+                                   CanonicalRHS, CanonicalFoundLHS,
+                                   CanonicalFoundRHS);
+    if (ICmpInst::isUnsigned(CanonicalPred) && isKnownNegative(CanonicalRHS))
+      // Use implication:
+      // x <s y && y <s 0 --> x <u y.
+      // If we can prove the left part, the right part is also proven.
+      return isImpliedCondOperands(CanonicalFoundPred, CanonicalLHS,
+                                   CanonicalRHS, CanonicalFoundLHS,
+                                   CanonicalFoundRHS);
+  }
 
   // Check if we can make progress by sharpening ranges.
   if (FoundPred == ICmpInst::ICMP_NE &&
diff --git a/llvm/test/Transforms/IndVarSimplify/outer_phi.ll b/llvm/test/Transforms/IndVarSimplify/outer_phi.ll
--- a/llvm/test/Transforms/IndVarSimplify/outer_phi.ll
+++ b/llvm/test/Transforms/IndVarSimplify/outer_phi.ll
@@ -463,7 +463,6 @@
 
 
 ; Same as test_01a, but non-negativity of %b is known without context.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05a(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05a(
 ; CHECK-NEXT:  entry:
@@ -477,8 +476,7 @@
 ; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ult i32 [[IV]], [[B]]
 ; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp slt i32 [[IV]], [[B]]
-; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -527,7 +525,6 @@
 }
 
 ; Similar to test_05a, but inverted 2nd condition.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05b(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05b(
 ; CHECK-NEXT:  entry:
@@ -541,8 +538,7 @@
 ; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ult i32 [[IV]], [[B]]
 ; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp sgt i32 [[B]], [[IV]]
-; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -591,7 +587,6 @@
 }
 
 ; We should prove implication: iv <s b, b <s 0 => iv <u b.
-; FIXME: Can remove 2nd check
 define i32 @test_05c(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05c(
 ; CHECK-NEXT:  entry:
@@ -605,8 +600,7 @@
 ; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp slt i32 [[IV]], [[B]]
 ; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ult i32 [[IV]], [[B]]
-; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -655,7 +649,6 @@
 }
 
 ; Same as test_05c, but 2nd condition reversed.
-; FIXME: Can remove 2nd check
 define i32 @test_05d(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05d(
 ; CHECK-NEXT:  entry:
@@ -669,8 +662,7 @@
 ; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp slt i32 [[IV]], [[B]]
 ; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ugt i32 [[B]], [[IV]]
-; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -720,7 +712,6 @@
 
 
 ; Same as test_05a, but 1st condition inverted.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05e(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05e(
 ; CHECK-NEXT:  entry:
@@ -734,8 +725,7 @@
 ; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ugt i32 [[B]], [[IV]]
 ; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp slt i32 [[IV]], [[B]]
-; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -784,7 +774,6 @@
 }
 
 ; Same as test_05b, but 1st condition inverted.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05f(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05f(
 ; CHECK-NEXT:  entry:
@@ -798,8 +787,7 @@
 ; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ugt i32 [[B]], [[IV]]
 ; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp sgt i32 [[B]], [[IV]]
-; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -848,7 +836,6 @@
 }
 
 ; Same as test_05c, but 1st condition inverted.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05g(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05g(
 ; CHECK-NEXT:  entry:
@@ -862,8 +849,7 @@
 ; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp sgt i32 [[B]], [[IV]]
 ; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ult i32 [[IV]], [[B]]
-; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()
@@ -912,7 +898,6 @@
 }
 
 ; Same as test_05d, but 1st condition inverted.
-; FIXME: We can remove 2nd check in loop.
 define i32 @test_05h(i32 %a, i32* %bp) {
 ; CHECK-LABEL: @test_05h(
 ; CHECK-NEXT:  entry:
@@ -926,8 +911,7 @@
 ; CHECK-NEXT:    [[SIGNED_COND:%.*]] = icmp sgt i32 [[B]], [[IV]]
 ; CHECK-NEXT:    br i1 [[SIGNED_COND]], label [[INNER_1:%.*]], label [[SIDE_EXIT:%.*]]
 ; CHECK:       inner.1:
-; CHECK-NEXT:    [[UNSIGNED_COND:%.*]] = icmp ugt i32 [[B]], [[IV]]
-; CHECK-NEXT:    br i1 [[UNSIGNED_COND]], label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
+; CHECK-NEXT:    br i1 true, label [[INNER_BACKEDGE]], label [[SIDE_EXIT]]
 ; CHECK:       inner.backedge:
 ; CHECK-NEXT:    [[IV_NEXT]] = add nuw nsw i32 [[IV]], 1
 ; CHECK-NEXT:    [[INNER_LOOP_COND:%.*]] = call i1 @cond()