Theorem mpteq2dv

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 23-Aug-2014)

	Ref	Expression
Hypothesis	mpteq2dv.1	|- ( ph -> B = C )
Assertion	mpteq2dv	|- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) )

Proof

Step	Hyp	Ref	Expression
1		mpteq2dv.1	|- ( ph -> B = C )
2	1	adantr	|- ( ( ph /\ x e. A ) -> B = C )
3	2	mpteq2dva	|- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) )