Theorem mpteq1d

Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 11-Jun-2016)

	Ref	Expression
Hypothesis	mpteq1d.1	|- ( ph -> A = B )
Assertion	mpteq1d	|- ( ph -> ( x e. A |-> C ) = ( x e. B |-> C ) )

Proof

Step	Hyp	Ref	Expression
1		mpteq1d.1	|- ( ph -> A = B )
2		mpteq1	|- ( A = B -> ( x e. A |-> C ) = ( x e. B |-> C ) )
3	1 2	syl	|- ( ph -> ( x e. A |-> C ) = ( x e. B |-> C ) )