diff --git a/src/backend/optimizer/util/predtest.c b/src/backend/optimizer/util/predtest.c
index d9e49d127e1a0a0cc2308a8b48479d68e75f6e91..7e86ca974be27ba59f00e366bcaa9a9fa4c2e358 100644
--- a/src/backend/optimizer/util/predtest.c
+++ b/src/backend/optimizer/util/predtest.c
@@ -1028,6 +1028,8 @@ arrayexpr_cleanup_fn(PredIterInfo info)
  * "foo" is NULL, which we can take as equivalent to FALSE because we know
  * we are within an AND/OR subtree of a WHERE clause.  (Again, "foo" is
  * already known immutable, so the clause will certainly always fail.)
+ * Also, if the clause is just "foo" (meaning it's a boolean variable),
+ * the predicate is implied since the clause can't be true if "foo" is NULL.
  *
  * Finally, if both clauses are binary operator expressions, we may be able
  * to prove something using the system's knowledge about operators; those
@@ -1061,6 +1063,8 @@ predicate_implied_by_simple_clause(Expr *predicate, Node *clause)
 				list_member_strip(((FuncExpr *) clause)->args, nonnullarg) &&
 				func_strict(((FuncExpr *) clause)->funcid))
 				return true;
+			if (equal(clause, nonnullarg))
+				return true;
 		}
 		return false;			/* we can't succeed below... */
 	}