Description: Change the bound variable of a class substitution using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvsbcvw when possible. (Contributed by NM, 30-Sep-2008) (Revised by Mario Carneiro, 13-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbvsbcv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | cbvsbcv | |- ( [. A / x ]. ph <-> [. A / y ]. ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbvsbcv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | nfv | |- F/ y ph |
|
| 3 | nfv | |- F/ x ps |
|
| 4 | 2 3 1 | cbvsbc | |- ( [. A / x ]. ph <-> [. A / y ]. ps ) |