Metamath Proof Explorer

Theorem cbvmptg

Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. Usage of this theorem is discouraged because it depends on ax-13 . See cbvmpt for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by NM, 11-Sep-2011) (New usage is discouraged.)

Ref Expression
Hypotheses cbvmptg.1 _ y B
cbvmptg.2 _ x C
cbvmptg.3 x = y B = C
Assertion cbvmptg x A B = y A C


Step Hyp Ref Expression
1 cbvmptg.1 _ y B
2 cbvmptg.2 _ x C
3 cbvmptg.3 x = y B = C
4 nfcv _ x A
5 nfcv _ y A
6 4 5 1 2 3 cbvmptfg x A B = y A C