diff --git a/tensorflow/core/framework/common_shape_fns.cc b/tensorflow/core/framework/common_shape_fns.cc
index 216002ad8e7..b9efddf4cdb 100644
--- a/tensorflow/core/framework/common_shape_fns.cc
+++ b/tensorflow/core/framework/common_shape_fns.cc
@@ -1955,6 +1955,7 @@ Status BroadcastBinaryOpOutputShapeFnHelper(InferenceContext* c,
       // in C++ op code, we must still assert that the unknown dim is either 1
       // or the same as the known dim.
       // - If either dimension is 1, the other dimension is the output.
+      // - If both are unknown then dimension is unknown
       if (c->Value(dim_x) > 1) {
         if (!incompatible_shape_error) {
           *out = c->UnknownShape();
@@ -1973,6 +1974,8 @@ Status BroadcastBinaryOpOutputShapeFnHelper(InferenceContext* c,
         dims.push_back(dim_x);
       } else if (dim_y.SameHandle(dim_x)) {
         dims.push_back(dim_x);
+      } else if (!c->ValueKnown(dim_x) && !c->ValueKnown(dim_y)) {
+        dims.push_back(c->UnknownDim());
       } else {
         if (!incompatible_shape_error) {
           *out = c->UnknownShape();
diff --git a/tensorflow/core/ops/math_ops_test.cc b/tensorflow/core/ops/math_ops_test.cc
index 5c69a2a7f1c..2b65f88042c 100644
--- a/tensorflow/core/ops/math_ops_test.cc
+++ b/tensorflow/core/ops/math_ops_test.cc
@@ -120,7 +120,7 @@ TEST(MathOpsTest, BroadcastBinaryOps_ShapeFn) {
     INFER_OK(op, "[1];[?]", "[d1_0]");
     INFER_OK(op, "[?];[2]", incompatible_shape_error ? "[d1_0]" : "?");
     INFER_OK(op, "[2];[?]", incompatible_shape_error ? "[d0_0]" : "?");
-    INFER_OK(op, "[?];[?]", incompatible_shape_error ? "[?]" : "?");
+    INFER_OK(op, "[?];[?]", "[?]");
     INFER_OK(op, "[];[?]", "[d1_0]");
     INFER_OK(op, "[?];[]", "[d0_0]");
 
@@ -604,4 +604,22 @@ TEST(MathOpsTest, SobolSample) {
 
   INFER_OK(op, "[];[];[]", "[?,?]");
 }
+
+TEST(MathOpsTest, EqualOp) {
+  ShapeInferenceTestOp op("Equal");
+  AddNodeAttr("incompatible_shape_error", true, &op.node_def);
+
+  INFER_OK(op, "?;?", "?");
+  INFER_OK(op, "[1,2];?", "?");
+  INFER_OK(op, "?;[1,2]", "?");
+
+  INFER_OK(op, "[1,2,3];[1]", "[d0_0,d0_1,d0_2]");
+  INFER_OK(op, "[?,2,1];[1,3]", "[d0_0,d0_1,d1_1]");
+  INFER_OK(op, "[1,?,3];[3,1]", "[d0_0,d1_0,d0_2]");
+  INFER_OK(op, "[1,2,3];[2,1,3]", "[d1_0,d0_1,d0_2]");
+
+  // Note: Test case for GitHub issue 40471
+  INFER_OK(op, "[?,10,1];[?,1,4]", "[?,d0_1,d1_2]");
+  INFER_OK(op, "[10,?,1];[1,?,4]", "[d0_0,?,d1_2]");
+}
 }  // end namespace tensorflow