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 y φ
cbvral.2 x ψ
cbvral.3 x = y φ ψ
Assertion cbvral x A φ y A ψ


Step Hyp Ref Expression
1 cbvral.1 y φ
2 cbvral.2 x ψ
3 cbvral.3 x = y φ ψ
4 nfcv _ x A
5 nfcv _ y A
6 4 5 1 2 3 cbvralf x A φ y A ψ