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
@@ -2690,6 +2690,9 @@
     return nullptr;
 
   // A boolean compared to true/false can be simplified in 14 out of the 20
+
+  Value *X;
+
   // (10 predicates * 2 constants) possible combinations. Cases not handled here
   // require a 'not' of the LHS, so those must be transformed in InstCombine.
   if (match(RHS, m_Zero())) {
@@ -2699,6 +2702,13 @@
     case CmpInst::ICMP_SLT: // X <s  0 -> X
       return LHS;
 
+    case CmpInst::ICMP_EQ:
+      // (X ^ 1) == 0 -> X
+      if (match(LHS, m_Xor(m_Value(X), m_One()))) {
+        return X;
+      }
+      break;
+
     case CmpInst::ICMP_ULT: // X <u  0 -> false
     case CmpInst::ICMP_SGT: // X >s  0 -> false
       return getFalse(ITy);
diff --git a/llvm/test/Transforms/InstSimplify/icmp.ll b/llvm/test/Transforms/InstSimplify/icmp.ll
--- a/llvm/test/Transforms/InstSimplify/icmp.ll
+++ b/llvm/test/Transforms/InstSimplify/icmp.ll
@@ -186,6 +186,16 @@
   ret i1 %cmp
 }
 
+define i1 @not_cmp_equal(i1 %x) {
+; CHECK-LABEL: @not_cmp_equal(
+; CHECK-NEXT:    ret i1 %x
+;
+  %not = xor i1 %x, true
+  %t0 = sext i1 %not to i32
+  %cmp = icmp eq i32 %t0, 0
+  ret i1 %cmp
+}
+
 ; Don't crash matching recurrences/invertible ops.
 
 define void @PR50191(i32 %x) {