Description: This is the all imporant formula which allows us to apply Frege-style definitions and explore their consequences. A closed form of biimpri . Proposition 57 of Frege1879 p. 51. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege57aid | |- ( ( ph <-> ps ) -> ( ps -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege52aid | |- ( ( ps <-> ph ) -> ( ps -> ph ) ) |
|
| 2 | frege56aid | |- ( ( ( ps <-> ph ) -> ( ps -> ph ) ) -> ( ( ph <-> ps ) -> ( ps -> ph ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph <-> ps ) -> ( ps -> ph ) ) |