Theorem mpoeq123i

Description: An equality inference for the maps-to notation. (Contributed by NM, 15-Jul-2013)

	Ref	Expression
Hypotheses	mpoeq123i.1	|- A = D
	mpoeq123i.2	|- B = E
	mpoeq123i.3	|- C = F
Assertion	mpoeq123i	|- ( x e. A , y e. B |-> C ) = ( x e. D , y e. E |-> F )

Proof

Step	Hyp	Ref	Expression
1		mpoeq123i.1	|- A = D
2		mpoeq123i.2	|- B = E
3		mpoeq123i.3	|- C = F
4	1	a1i	|- ( T. -> A = D )
5	2	a1i	|- ( T. -> B = E )
6	3	a1i	|- ( T. -> C = F )
7	4 5 6	mpoeq123dv	|- ( T. -> ( x e. A , y e. B |-> C ) = ( x e. D , y e. E |-> F ) )
8	7	mptru	|- ( x e. A , y e. B |-> C ) = ( x e. D , y e. E |-> F )