mysql> CREATE TABLE t1
 -> (
 -> CHECK (c1 <> c2),
 -> c1 INT CHECK (c1 > 10),
 -> c2 INT CONSTRAINT c2_positive CHECK (c2 > 0),
 -> c3 INT CHECK (c3 < 100),
 -> CONSTRAINT c1_nonzero CHECK (c1 <> 0),
 -> CHECK (c1 > c3)
 -> );
Query OK, 0 rows affected (0.03 sec)

mysql> ALTER TABLE t1 ADD CONSTRAINT c3_nonzero CHECK ((c3<>0));
Query OK, 0 rows affected (0.16 sec)
Records: 0 Duplicates: 0 Warnings: 0

mysql> ALTER TABLE t1 DROP CONSTRAINT c3_nonzero;
Query OK, 0 rows affected (0.02 sec)
Records: 0 Duplicates: 0 Warnings: 0

mysql> SHOW CREATE TABLE t1\G
*************************** 1. row ***************************
 Table: t1
Create Table: CREATE TABLE `t1` (
 `c1` int DEFAULT NULL,
 `c2` int DEFAULT NULL,
 `c3` int DEFAULT NULL,
 CONSTRAINT `c1_nonzero` CHECK ((`c1` <> 0)),
 CONSTRAINT `c2_positive` CHECK ((`c2` > 0)),
 CONSTRAINT `t1_chk_1` CHECK ((`c1` <> `c2`)),
 CONSTRAINT `t1_chk_2` CHECK ((`c1` > 10)),
 CONSTRAINT `t1_chk_3` CHECK ((`c3` < 100)),
 CONSTRAINT `t1_chk_4` CHECK ((`c1` > `c3`))
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_0900_ai_ci
1 row in set (0.00 sec)

mysql> SELECT * FROM information_schema.table_constraints WHERE table_name='t1';
+--------------------+-------------------+-----------------+--------------+------------+-----------------+----------+
| CONSTRAINT_CATALOG | CONSTRAINT_SCHEMA | CONSTRAINT_NAME | TABLE_SCHEMA | TABLE_NAME | CONSTRAINT_TYPE | ENFORCED |
+--------------------+-------------------+-----------------+--------------+------------+-----------------+----------+
| def | test | c1_nonzero | test | t1 | CHECK | YES |
| def | test | c2_positive | test | t1 | CHECK | YES |
| def | test | t1_chk_1 | test | t1 | CHECK | YES |
| def | test | t1_chk_2 | test | t1 | CHECK | YES |
| def | test | t1_chk_3 | test | t1 | CHECK | YES |
| def | test | t1_chk_4 | test | t1 | CHECK | YES |
+--------------------+-------------------+-----------------+--------------+------------+-----------------+----------+
6 rows in set (0.00 sec)

mysql> SELECT * FROM information_schema.check_constraints WHERE constraint_name='c1_nonzero';
+--------------------+-------------------+-----------------+--------------+
| CONSTRAINT_CATALOG | CONSTRAINT_SCHEMA | CONSTRAINT_NAME | CHECK_CLAUSE |
+--------------------+-------------------+-----------------+--------------+
| def | test | c1_nonzero | (`c1` <> 0) |
+--------------------+-------------------+-----------------+--------------+
1 row in set (0.00 sec)

mysql> insert into t1 values(0,0,0);
ERROR 3819 (HY000): Check constraint 'c1_nonzero' is violated.