Description: Change the bound variable of a class substitution using implicit substitution. Version of cbvsbcv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 30-Sep-2008) (Revised by Gino Giotto, 10-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbvsbcvw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | cbvsbcvw | |- ( [. A / x ]. ph <-> [. A / y ]. ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbvsbcvw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | nfv | |- F/ y ph |
|
| 3 | nfv | |- F/ x ps |
|
| 4 | 2 3 1 | cbvsbcw | |- ( [. A / x ]. ph <-> [. A / y ]. ps ) |