Description: Generalization of antecedent. A trivial weak version of sps avoiding ax-12 . (Contributed by SN, 13-Nov-2025) (Proof shortened by WL, 19-Nov-2025)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | spsv.1 | |- ( ph -> ps ) |
|
| Assertion | spsv | |- ( A. x ph -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spsv.1 | |- ( ph -> ps ) |
|
| 2 | 1 | a1i | |- ( x = y -> ( ph -> ps ) ) |
| 3 | 2 | spimvw | |- ( A. x ph -> ps ) |