Metamath Proof Explorer

Theorem fneq12

Description: Equality theorem for function predicate with domain. (Contributed by Thierry Arnoux, 31-Jan-2017)

Ref Expression
Assertion fneq12 
|- ( ( F = G /\ A = B ) -> ( F Fn A <-> G Fn B ) )

Proof

Step Hyp Ref Expression
1 simpl 
 |-  ( ( F = G /\ A = B ) -> F = G )
2 simpr 
 |-  ( ( F = G /\ A = B ) -> A = B )
3 1 2 fneq12d 
 |-  ( ( F = G /\ A = B ) -> ( F Fn A <-> G Fn B ) )