Description: Implicit substitution of y for x into a theorem. Version of chvarv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 20-Apr-1994) (Revised by BJ, 31-May-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | chvarvv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| chvarvv.2 | |- ph |
||
| Assertion | chvarvv | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | chvarvv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | chvarvv.2 | |- ph |
|
| 3 | 1 | spvv | |- ( A. x ph -> ps ) |
| 4 | 3 2 | mpg | |- ps |