Metamath Proof Explorer


Theorem cbvral

Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvralw when possible. (Contributed by NM, 31-Jul-2003) (New usage is discouraged.)

Ref Expression
Hypotheses cbvral.1 yφ
cbvral.2 xψ
cbvral.3 x=yφψ
Assertion cbvral xAφyAψ

Proof

Step Hyp Ref Expression
1 cbvral.1 yφ
2 cbvral.2 xψ
3 cbvral.3 x=yφψ
4 nfcv _xA
5 nfcv _yA
6 4 5 1 2 3 cbvralf xAφyAψ