Metamath Proof Explorer

Theorem cbvrexw

Description: Rule used to change bound variables, using implicit substitution. Version of cbvrex with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 31-Jul-2003) (Revised by Gino Giotto, 10-Jan-2024)

Ref Expression
Hypotheses cbvralw.1 y φ
cbvralw.2 x ψ
cbvralw.3 x = y φ ψ
Assertion cbvrexw x A φ y A ψ


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