diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAddSub.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAddSub.cpp
index 318992b55e4f9f..90b1c133461a40 100644
--- a/llvm/lib/Transforms/InstCombine/InstCombineAddSub.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAddSub.cpp
@@ -2191,8 +2191,15 @@ Instruction *InstCombinerImpl::visitSub(BinaryOperator &I) {
 
   // ((X - Y) - Op1)  -->  X - (Y + Op1)
   if (match(Op0, m_OneUse(m_Sub(m_Value(X), m_Value(Y))))) {
-    Value *Add = Builder.CreateAdd(Y, Op1);
-    return BinaryOperator::CreateSub(X, Add);
+    OverflowingBinaryOperator *LHSSub = cast<OverflowingBinaryOperator>(Op0);
+    bool HasNUW = I.hasNoUnsignedWrap() && LHSSub->hasNoUnsignedWrap();
+    bool HasNSW = HasNUW && I.hasNoSignedWrap() && LHSSub->hasNoSignedWrap();
+    Value *Add = Builder.CreateAdd(Y, Op1, "", /* HasNUW */ HasNUW,
+                                   /* HasNSW */ HasNSW);
+    BinaryOperator *Sub = BinaryOperator::CreateSub(X, Add);
+    Sub->setHasNoUnsignedWrap(HasNUW);
+    Sub->setHasNoSignedWrap(HasNSW);
+    return Sub;
   }
 
   // (~X) - (~Y) --> Y - X
diff --git a/llvm/test/Transforms/InstCombine/sub-from-sub.ll b/llvm/test/Transforms/InstCombine/sub-from-sub.ll
index 7976cdc970b9c5..7b9e2fe4e6cdf2 100644
--- a/llvm/test/Transforms/InstCombine/sub-from-sub.ll
+++ b/llvm/test/Transforms/InstCombine/sub-from-sub.ll
@@ -17,14 +17,82 @@ define i8 @t0(i8 %x, i8 %y, i8 %z) {
   ret i8 %r
 }
 
-; No flags are propagated
+; NSW/NUW flags are propagated
 define i8 @t1_flags(i8 %x, i8 %y, i8 %z) {
 ; CHECK-LABEL: @t1_flags(
+; CHECK-NEXT:    [[TMP1:%.*]] = add nuw nsw i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub nuw nsw i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub nuw nsw i8 %x, %y
+  %r = sub nuw nsw i8 %o0, %z
+  ret i8 %r
+}
+
+; NUW flags are propagated
+define i8 @t1_flags_nuw_only(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_nuw_only(
+; CHECK-NEXT:    [[TMP1:%.*]] = add nuw i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub nuw i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub nuw i8 %x, %y
+  %r = sub nuw i8 %o0, %z
+  ret i8 %r
+}
+
+; Negative tests
+define i8 @t1_flags_sub_nsw_sub(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_sub_nsw_sub(
+; CHECK-NEXT:    [[TMP1:%.*]] = add i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub nsw i8 %x, %y
+  %r = sub i8 %o0, %z
+  ret i8 %r
+}
+
+define i8 @t1_flags_nuw_first(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_nuw_first(
+; CHECK-NEXT:    [[TMP1:%.*]] = add i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub nuw i8 %x, %y
+  %r = sub i8 %o0, %z
+  ret i8 %r
+}
+
+define i8 @t1_flags_nuw_second(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_nuw_second(
+; CHECK-NEXT:    [[TMP1:%.*]] = add i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub i8 %x, %y
+  %r = sub nuw i8 %o0, %z
+  ret i8 %r
+}
+
+define i8 @t1_flags_nuw_nsw_first(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_nuw_nsw_first(
 ; CHECK-NEXT:    [[TMP1:%.*]] = add i8 [[Y:%.*]], [[Z:%.*]]
 ; CHECK-NEXT:    [[R:%.*]] = sub i8 [[X:%.*]], [[TMP1]]
 ; CHECK-NEXT:    ret i8 [[R]]
 ;
   %o0 = sub nuw nsw i8 %x, %y
+  %r = sub i8 %o0, %z
+  ret i8 %r
+}
+
+define i8 @t1_flags_nuw_nsw_second(i8 %x, i8 %y, i8 %z) {
+; CHECK-LABEL: @t1_flags_nuw_nsw_second(
+; CHECK-NEXT:    [[TMP1:%.*]] = add i8 [[Y:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[R:%.*]] = sub i8 [[X:%.*]], [[TMP1]]
+; CHECK-NEXT:    ret i8 [[R]]
+;
+  %o0 = sub i8 %x, %y
   %r = sub nuw nsw i8 %o0, %z
   ret i8 %r
 }