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 chvarvv if possible. (Contributed by NM, 20-Apr-1994) (Proof shortened by Wolf Lammen, 22-Apr-2018) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | chvarv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| chvarv.2 | |- ph |
||
| Assertion | chvarv | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | chvarv.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | chvarv.2 | |- ph |
|
| 3 | nfv | |- F/ x ps |
|
| 4 | 3 1 2 | chvar | |- ps |