diff --git a/std/typecons.d b/std/typecons.d
index 6f4fa35bc08..8d0b9bf55b2 100644
--- a/std/typecons.d
+++ b/std/typecons.d
@@ -2128,6 +2128,18 @@ if (is(T == class) || is(T == interface) || isAssociativeArray!T)
         }
     }
 
+    bool opEquals()(auto ref const(typeof(this)) rhs) const
+    {
+        // Must forward explicitly because 'stripped' is part of a union.
+        // The necessary 'toHash' is forwarded to the class via alias this.
+        return stripped == rhs.stripped;
+    }
+
+    bool opEquals(const(U) rhs) const
+    {
+        return stripped == rhs;
+    }
+
     alias get this;
 }
 
@@ -2206,6 +2218,61 @@ if (is(T == class) || is(T == interface) || isDynamicArray!T || isAssociativeArr
     static assert(!__traits(compiles, &r.get()));
 }
 
+@safe unittest
+{
+    class CustomToHash
+    {
+        override size_t toHash() const nothrow @trusted { return 42; }
+    }
+    Rebindable!(immutable(CustomToHash)) a = new immutable CustomToHash();
+    assert(a.toHash() == 42, "Rebindable!A should offer toHash()"
+        ~ " by forwarding to A.toHash().");
+}
+
+@system unittest // issue 18615: Rebindable!A should use A.opEquals
+{
+    class CustomOpEq
+    {
+        int x;
+        override bool opEquals(Object rhsObj)
+        {
+            if (auto rhs = cast(const(CustomOpEq)) rhsObj)
+                return this.x == rhs.x;
+            else
+                return false;
+        }
+    }
+    CustomOpEq a = new CustomOpEq();
+    CustomOpEq b = new CustomOpEq();
+    assert(a !is b);
+    assert(a == b, "a.x == b.x should be true (0 == 0).");
+
+    Rebindable!(const(CustomOpEq)) ra = a;
+    Rebindable!(const(CustomOpEq)) rb = b;
+    assert(ra !is rb);
+    assert(ra == rb, "Rebindable should use CustomOpEq's opEquals, not 'is'.");
+    assert(ra == b, "Rebindable!(someQualifier(A)) should be comparable"
+        ~ " against const(A) via A.opEquals.");
+    assert(a == rb, "Rebindable!(someQualifier(A)) should be comparable"
+        ~ " against const(A) via A.opEquals.");
+
+    b.x = 1;
+    assert(a != b);
+    assert(ra != b, "Rebindable!(someQualifier(A)) should be comparable"
+        ~ " against const(A) via A.opEquals.");
+    assert(a != rb, "Rebindable!(someQualifier(A)) should be comparable"
+        ~ " against const(A) via A.opEquals.");
+
+    Rebindable!(const(Object)) o1 = new Object();
+    Rebindable!(const(Object)) o2 = new Object();
+    assert(o1 !is o2);
+    assert(o1 == o1, "When the class doesn't provide its own opEquals,"
+        ~ " Rebindable treats 'a == b' as 'a is b' like Object.opEquals.");
+    assert(o1 != o2, "When the class doesn't provide its own opEquals,"
+        ~ " Rebindable treats 'a == b' as 'a is b' like Object.opEquals.");
+    assert(o1 != new Object(), "Rebindable!(const(Object)) should be"
+        ~ " comparable against Object itself and use Object.opEquals.");
+}
 /**
 Convenience function for creating a `Rebindable` using automatic type
 inference.