Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by Mario Carneiro, 3-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | opelvvg | |- ( ( A e. V /\ B e. W ) -> <. A , B >. e. ( _V X. _V ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex | |- ( A e. V -> A e. _V ) |
|
2 | elex | |- ( B e. W -> B e. _V ) |
|
3 | opelxpi | |- ( ( A e. _V /\ B e. _V ) -> <. A , B >. e. ( _V X. _V ) ) |
|
4 | 1 2 3 | syl2an | |- ( ( A e. V /\ B e. W ) -> <. A , B >. e. ( _V X. _V ) ) |