diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -2706,6 +2706,14 @@
   // A boolean compared to true/false can be simplified in 14 out of the 20
   // (10 predicates * 2 constants) possible combinations. Cases not handled here
   // require a 'not' of the LHS, so those must be transformed in InstCombine.
+
+  auto ExtractNotLHS = [](Value *V) -> Value * {
+    Value *X;
+    if (match(V, m_Xor(m_Value(X), m_One())))
+      return X;
+    return nullptr;
+  };
+
   if (match(RHS, m_Zero())) {
     switch (Pred) {
     case CmpInst::ICMP_NE:  // X !=  0 -> X
@@ -2713,6 +2721,12 @@
     case CmpInst::ICMP_SLT: // X <s  0 -> X
       return LHS;
 
+    case CmpInst::ICMP_EQ:  // not(X) ==  0 -> X != 0 -> X
+    case CmpInst::ICMP_ULE: // not(X) <=u 0 -> X >u 0 -> X
+    case CmpInst::ICMP_SGE: // not(X) >=s 0 -> X <s 0 -> X
+      if (Value *X = ExtractNotLHS(LHS))
+        return X;
+
     case CmpInst::ICMP_ULT: // X <u  0 -> false
     case CmpInst::ICMP_SGT: // X >s  0 -> false
       return getFalse(ITy);
@@ -2730,6 +2744,12 @@
     case CmpInst::ICMP_SLE: // X <=s -1 -> X
       return LHS;
 
+    case CmpInst::ICMP_NE:  // not(X) !=  1 -> X ==   1 -> X
+    case CmpInst::ICMP_ULT: // not(X) <=u 1 -> X >=u  1 -> X
+    case CmpInst::ICMP_SGT: // not(X) >s  1 -> X <=s -1 -> X
+      if (Value *X = ExtractNotLHS(LHS))
+        return X;
+
     case CmpInst::ICMP_UGT: // X >u   1 -> false
     case CmpInst::ICMP_SLT: // X <s  -1 -> false
       return getFalse(ITy);
diff --git a/llvm/test/Transforms/InstSimplify/icmp-not-bool-constant.ll b/llvm/test/Transforms/InstSimplify/icmp-not-bool-constant.ll
--- a/llvm/test/Transforms/InstSimplify/icmp-not-bool-constant.ll
+++ b/llvm/test/Transforms/InstSimplify/icmp-not-bool-constant.ll
@@ -17,9 +17,7 @@
 
 define <2 x i1> @eq_f_not(<2 x i1> %a) {
 ; CHECK-LABEL: @eq_f_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp eq <2 x i1> [[NOT]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp eq <2 x i1> %not, <i1 false, i1 false>
@@ -28,9 +26,7 @@
 
 define <2 x i1> @ne_t_not(<2 x i1> %a) {
 ; CHECK-LABEL: @ne_t_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp ne <2 x i1> [[NOT]], <i1 true, i1 true>
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp ne <2 x i1> %not, <i1 true, i1 true>
@@ -68,9 +64,7 @@
 
 define <2 x i1> @ult_t_not(<2 x i1> %a) {
 ; CHECK-LABEL: @ult_t_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp ult <2 x i1> [[NOT]], <i1 true, i1 true>
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp ult <2 x i1> %not, <i1 true, i1 true>
@@ -88,9 +82,7 @@
 
 define <2 x i1> @sgt_t_not(<2 x i1> %a) {
 ; CHECK-LABEL: @sgt_t_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp sgt <2 x i1> [[NOT]], <i1 true, i1 true>
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp sgt <2 x i1> %not, <i1 true, i1 true>
@@ -155,9 +147,7 @@
 
 define <2 x i1> @ule_f_not(<2 x i1> %a) {
 ; CHECK-LABEL: @ule_f_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp ule <2 x i1> [[NOT]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp ule <2 x i1> %not, <i1 false, i1 false>
@@ -175,9 +165,7 @@
 
 define <2 x i1> @sge_f_not(<2 x i1> %a) {
 ; CHECK-LABEL: @sge_f_not(
-; CHECK-NEXT:    [[NOT:%.*]] = xor <2 x i1> [[A:%.*]], <i1 true, i1 true>
-; CHECK-NEXT:    [[R:%.*]] = icmp sge <2 x i1> [[NOT]], zeroinitializer
-; CHECK-NEXT:    ret <2 x i1> [[R]]
+; CHECK-NEXT:    ret <2 x i1> [[A:%.*]]
 ;
   %not = xor <2 x i1> %a, <i1 true, i1 true>
   %r = icmp sge <2 x i1> %not, <i1 false, i1 false>