Metamath Proof Explorer

Theorem cbvalv

Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . See cbvalvw for a version requiring fewer axioms, to be preferred when sufficient. (Contributed by NM, 5-Aug-1993) Remove dependency on ax-10 , shorten. (Revised by Wolf Lammen, 11-Sep-2023) (New usage is discouraged.)

Ref Expression
Hypothesis cbvalv.1 x = y φ ψ
Assertion cbvalv x φ y ψ


Step Hyp Ref Expression
1 cbvalv.1 x = y φ ψ
2 nfv y φ
3 nfv x ψ
4 2 3 1 cbval x φ y ψ