Description: Implicit substitution of y for x into a theorem. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker chvarfv if possible. (Contributed by Raph Levien, 9-Jul-2003) (Revised by Mario Carneiro, 3-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | chvar.1 | |- F/ x ps |
|
| chvar.2 | |- ( x = y -> ( ph <-> ps ) ) |
||
| chvar.3 | |- ph |
||
| Assertion | chvar | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | chvar.1 | |- F/ x ps |
|
| 2 | chvar.2 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 3 | chvar.3 | |- ph |
|
| 4 | 2 | biimpd | |- ( x = y -> ( ph -> ps ) ) |
| 5 | 1 4 | spim | |- ( A. x ph -> ps ) |
| 6 | 5 3 | mpg | |- ps |