Theorem cbvmptvg

Description: Rule to change the bound variable in a maps-to function, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . See cbvmptv for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by Mario Carneiro, 19-Feb-2013) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		cbvmptvg.1	|- ( x = y -> B = C )
2		nfcv	|- F/_ y B
3		nfcv	|- F/_ x C
4	2 3 1	cbvmptg	|- ( x e. A |-> B ) = ( y e. A |-> C )