create table t1 (a int);
insert into t1 values (1),(2),(3);

create table t2 as select * from t1;

create table t_pk1 (a int primary key);
create table t_pk2 (a int primary key);

insert into t_pk1 select a from t1;
insert into t_pk2 select a from t1;

alter table t_pk1 add b int;
alter table t_pk2 add b int;

## Here t_pk1 is a constant table, and "t_pk1.b> 3" is a cheap constant condition that evaluates to FALSE:

MariaDB [j10]> explain select * from t_pk1, t2 where t_pk1.a=2 and t_pk1.b> 3 ;
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------------------------------------------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra                                               |
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------------------------------------------+
|  1 | SIMPLE      | NULL  | NULL | NULL          | NULL | NULL    | NULL | NULL | Impossible WHERE noticed after reading const tables |
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------------------------------------------+
1 row in set (0.00 sec)

# Now, let's add an expensive constant condition, and observe that we won't be getting "Impossible WHERE" anymore:

MariaDB [j10]> explain select * from t_pk1, t2 where t_pk1.a=2 and t_pk1.b> 3 and 2 > (select max(a) from t1);
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+
| id | select_type | table | type  | possible_keys | key     | key_len | ref   | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+
|  1 | PRIMARY     | t_pk1 | const | PRIMARY       | PRIMARY | 4       | const |    1 |       |
|  1 | PRIMARY     | t2    | ALL   | NULL          | NULL    | NULL    | NULL  |    3 |       |
|  2 | SUBQUERY    | t1    | ALL   | NULL          | NULL    | NULL    | NULL  |    3 |       |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+
3 rows in set (0.00 sec)