Theorem mpteq12i

Description: An equality inference for the maps-to notation. (Contributed by Scott Fenton, 27-Oct-2010) (Revised by Mario Carneiro, 16-Dec-2013)

	Ref	Expression
Hypotheses	mpteq12i.1	|- A = C
	mpteq12i.2	|- B = D
Assertion	mpteq12i	|- ( x e. A |-> B ) = ( x e. C |-> D )

Proof

Step	Hyp	Ref	Expression
1		mpteq12i.1	|- A = C
2		mpteq12i.2	|- B = D
3	1	a1i	|- ( T. -> A = C )
4	2	a1i	|- ( T. -> B = D )
5	3 4	mpteq12dv	|- ( T. -> ( x e. A |-> B ) = ( x e. C |-> D ) )
6	5	mptru	|- ( x e. A |-> B ) = ( x e. C |-> D )