diff --git a/src/backend/optimizer/util/appendinfo.c b/src/backend/optimizer/util/appendinfo.c
index f456b3b0a44..a72704da425 100644
--- a/src/backend/optimizer/util/appendinfo.c
+++ b/src/backend/optimizer/util/appendinfo.c
@@ -233,8 +233,9 @@ adjust_appendrel_attrs_mutator(Node *node,
 		 * You might think we need to adjust var->varnullingrels, but that
 		 * shouldn't need any changes.  It will contain outer-join relids,
 		 * while the transformation we are making affects only baserels.
-		 * Below, we just propagate var->varnullingrels into the translated
-		 * Var.
+		 * Below, we just merge var->varnullingrels into the translated Var.
+		 * (We must merge not just copy: the child Var could have some
+		 * nullingrel bits set already, and we mustn't drop those.)
 		 *
 		 * If var->varnullingrels isn't empty, and the translation wouldn't be
 		 * a Var, we have to fail.  One could imagine wrapping the translated
@@ -279,7 +280,12 @@ adjust_appendrel_attrs_mutator(Node *node,
 					elog(ERROR, "attribute %d of relation \"%s\" does not exist",
 						 var->varattno, get_rel_name(appinfo->parent_reloid));
 				if (IsA(newnode, Var))
-					((Var *) newnode)->varnullingrels = var->varnullingrels;
+				{
+					Var		   *newvar = (Var *) newnode;
+
+					newvar->varnullingrels = bms_add_members(newvar->varnullingrels,
+															 var->varnullingrels);
+				}
 				else if (var->varnullingrels != NULL)
 					elog(ERROR, "failed to apply nullingrels to a non-Var");
 				return newnode;
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 84e35981ed8..b6f86d9aaf0 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -4020,6 +4020,58 @@ where ss.x is null;
                      Output: 'bar'::text
 (12 rows)
 
+-- Test computation of varnullingrels when translating appendrel Var
+begin;
+create temp table t_append (a int not null, b int);
+insert into t_append values (1, 1);
+insert into t_append values (2, 3);
+explain (verbose, costs off)
+select t1.a, s.a from t_append t1
+  left join t_append t2 on t1.a = t2.b
+  join lateral (
+    select t1.a as a union all select t2.a as a
+  ) s on true
+where s.a is not null;
+                    QUERY PLAN                     
+---------------------------------------------------
+ Nested Loop
+   Output: t1.a, (t1.a)
+   ->  Merge Left Join
+         Output: t1.a, t2.a
+         Merge Cond: (t1.a = t2.b)
+         ->  Sort
+               Output: t1.a
+               Sort Key: t1.a
+               ->  Seq Scan on pg_temp.t_append t1
+                     Output: t1.a
+         ->  Sort
+               Output: t2.a, t2.b
+               Sort Key: t2.b
+               ->  Seq Scan on pg_temp.t_append t2
+                     Output: t2.a, t2.b
+   ->  Append
+         ->  Result
+               Output: t1.a
+               One-Time Filter: (t1.a IS NOT NULL)
+         ->  Result
+               Output: t2.a
+               One-Time Filter: (t2.a IS NOT NULL)
+(22 rows)
+
+select t1.a, s.a from t_append t1
+  left join t_append t2 on t1.a = t2.b
+  join lateral (
+    select t1.a as a union all select t2.a as a
+  ) s on true
+where s.a is not null;
+ a | a 
+---+---
+ 1 | 1
+ 1 | 1
+ 2 | 2
+(3 rows)
+
+rollback;
 --
 -- test inlining of immutable functions
 --
diff --git a/src/test/regress/sql/join.sql b/src/test/regress/sql/join.sql
index d6f646a1d50..dc4c5a9628f 100644
--- a/src/test/regress/sql/join.sql
+++ b/src/test/regress/sql/join.sql
@@ -1329,6 +1329,30 @@ select * from int4_tbl left join (
 ) ss(x) on true
 where ss.x is null;
 
+-- Test computation of varnullingrels when translating appendrel Var
+begin;
+
+create temp table t_append (a int not null, b int);
+insert into t_append values (1, 1);
+insert into t_append values (2, 3);
+
+explain (verbose, costs off)
+select t1.a, s.a from t_append t1
+  left join t_append t2 on t1.a = t2.b
+  join lateral (
+    select t1.a as a union all select t2.a as a
+  ) s on true
+where s.a is not null;
+
+select t1.a, s.a from t_append t1
+  left join t_append t2 on t1.a = t2.b
+  join lateral (
+    select t1.a as a union all select t2.a as a
+  ) s on true
+where s.a is not null;
+
+rollback;
+
 --
 -- test inlining of immutable functions
 --