Description: Implicit substitution of y for x into a theorem. Version of chvar with a disjoint variable condition, which does not require ax-13 . (Contributed by Raph Levien, 9-Jul-2003) (Revised by BJ, 31-May-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | chvarfv.nf | |- F/ x ps |
|
| chvarfv.1 | |- ( x = y -> ( ph <-> ps ) ) |
||
| chvarfv.2 | |- ph |
||
| Assertion | chvarfv | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | chvarfv.nf | |- F/ x ps |
|
| 2 | chvarfv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 3 | chvarfv.2 | |- ph |
|
| 4 | 2 | biimpd | |- ( x = y -> ( ph -> ps ) ) |
| 5 | 1 4 | spimfv | |- ( A. x ph -> ps ) |
| 6 | 5 3 | mpg | |- ps |