Description: Inference form of sbalex , avoiding ax-10 by using ax-gen . (Contributed by SN, 12-Aug-2025)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbalexi.1 | |- E. x ( x = y /\ ph ) |
|
| Assertion | sbalexi | |- A. x ( x = y -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbalexi.1 | |- E. x ( x = y /\ ph ) |
|
| 2 | ax12ev2 | |- ( E. x ( x = y /\ ph ) -> ( x = y -> ph ) ) |
|
| 3 | 1 2 | ax-mp | |- ( x = y -> ph ) |
| 4 | 3 | ax-gen | |- A. x ( x = y -> ph ) |