diff --git a/src/backend/optimizer/util/clauses.c b/src/backend/optimizer/util/clauses.c
index 7fb32a0710..5e791333cb 100644
--- a/src/backend/optimizer/util/clauses.c
+++ b/src/backend/optimizer/util/clauses.c
@@ -1511,6 +1511,31 @@ find_nonnullable_rels_walker(Node *node, bool top_level)
 			 expr->booltesttype == IS_NOT_UNKNOWN))
 			result = find_nonnullable_rels_walker((Node *) expr->arg, false);
 	}
+	else if (IsA(node, SubPlan))
+	{
+		SubPlan    *splan = (SubPlan *) node;
+
+		/*
+		 * For some types of SubPlan, we can infer strictness from Vars in the
+		 * testexpr (the LHS of the original SubLink).
+		 *
+		 * For ANY_SUBLINK, if the subquery produces zero rows, the result is
+		 * always FALSE.  If the subquery produces more than one row, the
+		 * per-row results of the testexpr are combined using OR semantics.
+		 * Hence ANY_SUBLINK can be strict only at top level, but there it's
+		 * as strict as the testexpr is.
+		 *
+		 * For ROWCOMPARE_SUBLINK, if the subquery produces zero rows, the
+		 * result is always NULL.  Otherwise, the result is as strict as the
+		 * testexpr is.  So we can check regardless of top_level.
+		 *
+		 * We can't prove anything for other sublink types (in particular,
+		 * note that ALL_SUBLINK will return TRUE if the subquery is empty).
+		 */
+		if ((top_level && splan->subLinkType == ANY_SUBLINK) ||
+			splan->subLinkType == ROWCOMPARE_SUBLINK)
+			result = find_nonnullable_rels_walker(splan->testexpr, top_level);
+	}
 	else if (IsA(node, PlaceHolderVar))
 	{
 		PlaceHolderVar *phv = (PlaceHolderVar *) node;
@@ -1736,6 +1761,15 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
 			 expr->booltesttype == IS_NOT_UNKNOWN))
 			result = find_nonnullable_vars_walker((Node *) expr->arg, false);
 	}
+	else if (IsA(node, SubPlan))
+	{
+		SubPlan    *splan = (SubPlan *) node;
+
+		/* See analysis in find_nonnullable_rels_walker */
+		if ((top_level && splan->subLinkType == ANY_SUBLINK) ||
+			splan->subLinkType == ROWCOMPARE_SUBLINK)
+			result = find_nonnullable_vars_walker(splan->testexpr, top_level);
+	}
 	else if (IsA(node, PlaceHolderVar))
 	{
 		PlaceHolderVar *phv = (PlaceHolderVar *) node;
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index b901d7299f..9358371072 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -4650,6 +4650,34 @@ select a.q2, b.q1
 
 reset enable_hashjoin;
 reset enable_nestloop;
+--
+-- test join strength reduction with a SubPlan providing the proof
+--
+explain (costs off)
+select a.unique1, b.unique2
+  from onek a left join onek b on a.unique1 = b.unique2
+  where b.unique2 = any (select q1 from int8_tbl c where c.q1 < b.unique1);
+                        QUERY PLAN                        
+----------------------------------------------------------
+ Hash Join
+   Hash Cond: (b.unique2 = a.unique1)
+   ->  Seq Scan on onek b
+         Filter: (SubPlan 1)
+         SubPlan 1
+           ->  Seq Scan on int8_tbl c
+                 Filter: (q1 < b.unique1)
+   ->  Hash
+         ->  Index Only Scan using onek_unique1 on onek a
+(9 rows)
+
+select a.unique1, b.unique2
+  from onek a left join onek b on a.unique1 = b.unique2
+  where b.unique2 = any (select q1 from int8_tbl c where c.q1 < b.unique1);
+ unique1 | unique2 
+---------+---------
+     123 |     123
+(1 row)
+
 --
 -- test join removal
 --
diff --git a/src/test/regress/sql/join.sql b/src/test/regress/sql/join.sql
index ccbbe5454c..a81c7dce7d 100644
--- a/src/test/regress/sql/join.sql
+++ b/src/test/regress/sql/join.sql
@@ -1603,6 +1603,19 @@ select a.q2, b.q1
 reset enable_hashjoin;
 reset enable_nestloop;
 
+--
+-- test join strength reduction with a SubPlan providing the proof
+--
+
+explain (costs off)
+select a.unique1, b.unique2
+  from onek a left join onek b on a.unique1 = b.unique2
+  where b.unique2 = any (select q1 from int8_tbl c where c.q1 < b.unique1);
+
+select a.unique1, b.unique2
+  from onek a left join onek b on a.unique1 = b.unique2
+  where b.unique2 = any (select q1 from int8_tbl c where c.q1 < b.unique1);
+
 --
 -- test join removal
 --