Metamath Proof Explorer


Theorem opprc1

Description: Expansion of an ordered pair when the first member is a proper class. See also opprc . (Contributed by NM, 10-Apr-2004) (Revised by Mario Carneiro, 26-Apr-2015)

Ref Expression
Assertion opprc1
|- ( -. A e. _V -> <. A , B >. = (/) )

Proof

Step Hyp Ref Expression
1 simpl
 |-  ( ( A e. _V /\ B e. _V ) -> A e. _V )
2 opprc
 |-  ( -. ( A e. _V /\ B e. _V ) -> <. A , B >. = (/) )
3 1 2 nsyl5
 |-  ( -. A e. _V -> <. A , B >. = (/) )