Metamath Proof Explorer


Theorem ovprc1

Description: The value of an operation when the first argument is a proper class. (Contributed by NM, 16-Jun-2004)

Ref Expression
Hypothesis ovprc1.1
|- Rel dom F
Assertion ovprc1
|- ( -. A e. _V -> ( A F B ) = (/) )

Proof

Step Hyp Ref Expression
1 ovprc1.1
 |-  Rel dom F
2 simpl
 |-  ( ( A e. _V /\ B e. _V ) -> A e. _V )
3 1 ovprc
 |-  ( -. ( A e. _V /\ B e. _V ) -> ( A F B ) = (/) )
4 2 3 nsyl5
 |-  ( -. A e. _V -> ( A F B ) = (/) )