Description: Theorem 19.23 of Margaris p. 90. See 19.23v for a version requiring fewer axioms. (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 19.23.1 | |- F/ x ps |
|
Assertion | 19.23 | |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.23.1 | |- F/ x ps |
|
2 | 19.23t | |- ( F/ x ps -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) ) |
|
3 | 1 2 | ax-mp | |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) |