Theorem nfmpt

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013)

	Ref	Expression
Hypotheses	nfmpt.1	|- F/_ x A
	nfmpt.2	|- F/_ x B
Assertion	nfmpt	|- F/_ x ( y e. A |-> B )

Proof

Step	Hyp	Ref	Expression
1		nfmpt.1	|- F/_ x A
2		nfmpt.2	|- F/_ x B
3		df-mpt	|- ( y e. A |-> B ) = { <. y , z >. | ( y e. A /\ z = B ) }
4	1	nfcri	|- F/ x y e. A
5	2	nfeq2	|- F/ x z = B
6	4 5	nfan	|- F/ x ( y e. A /\ z = B )
7	6	nfopab	|- F/_ x { <. y , z >. | ( y e. A /\ z = B ) }
8	3 7	nfcxfr	|- F/_ x ( y e. A |-> B )