Metamath Proof Explorer


Theorem cbvralv

Description: Change the bound variable of a restricted universal quantifier using implicit substitution. See cbvralvw based on fewer axioms , but extra disjoint variables. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvralvw when possible. (Contributed by NM, 28-Jan-1997) (New usage is discouraged.)

Ref Expression
Hypothesis cbvralv.1 x=yφψ
Assertion cbvralv xAφyAψ

Proof

Step Hyp Ref Expression
1 cbvralv.1 x=yφψ
2 nfv yφ
3 nfv xψ
4 2 3 1 cbvral xAφyAψ