Theorem cbvmptv

Description: Rule to change the bound variable in a maps-to function, using implicit substitution. (Contributed by Mario Carneiro, 19-Feb-2013) Add disjoint variable condition to avoid ax-13 . See cbvmptvg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 17-Jan-2024)

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

Proof

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