Theorem mpteq2dva

Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012)

	Ref	Expression
Hypothesis	mpteq2dva.1	|- ( ( ph /\ x e. A ) -> B = C )
Assertion	mpteq2dva	|- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) )

Proof

Step	Hyp	Ref	Expression
1		mpteq2dva.1	|- ( ( ph /\ x e. A ) -> B = C )
2		nfv	|- F/ x ph
3	2 1	mpteq2da	|- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) )