Description: Lemma for weak version of ax-12 . Uses only Tarski's FOL axiom schemes. In some cases, this lemma may lead to shorter proofs than ax12w . (Contributed by NM, 10-Apr-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ax12wlemw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | ax12wlem | |- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax12wlemw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | ax-5 | |- ( ps -> A. x ps ) |
|
| 3 | 1 2 | ax12i | |- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) ) |