Metamath Proof Explorer


Theorem cbvralsvwOLD

Description: Obsolete version of cbvralsvw as of 21-Aug-2025. (Contributed by NM, 20-Nov-2005) Avoid ax-13 . (Revised by GG, 10-Jan-2024) (Proof shortened by Wolf Lammen, 8-Mar-2025) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion cbvralsvwOLD
|- ( A. x e. A ph <-> A. y e. A [ y / x ] ph )

Proof

Step Hyp Ref Expression
1 nfv
 |-  F/ y ph
2 nfs1v
 |-  F/ x [ y / x ] ph
3 sbequ12
 |-  ( x = y -> ( ph <-> [ y / x ] ph ) )
4 1 2 3 cbvralw
 |-  ( A. x e. A ph <-> A. y e. A [ y / x ] ph )