Description: The first member of an ordered pair of classes in a Cartesian product belongs to first Cartesian product argument. (Contributed by NM, 28-May-2008) (Revised by Mario Carneiro, 26-Apr-2015)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | opelxp1 | |- ( <. A , B >. e. ( C X. D ) -> A e. C ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opelxp | |- ( <. A , B >. e. ( C X. D ) <-> ( A e. C /\ B e. D ) ) |
|
| 2 | 1 | simplbi | |- ( <. A , B >. e. ( C X. D ) -> A e. C ) |