Description: Theorem 19.23 of Margaris p. 90. See 19.23 . (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016) (Proof shortened by Wolf Lammen, 1-Jan-2018)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | 19.23h.1 | |- ( ps -> A. x ps ) |
|
| Assertion | 19.23h | |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.23h.1 | |- ( ps -> A. x ps ) |
|
| 2 | 1 | nf5i | |- F/ x ps |
| 3 | 2 | 19.23 | |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) |