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 ) |
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 ) |