Description: Add antecedent to ax-frege2 . Special case of rp-frege3g . Proposition 3 of Frege1879 p. 29. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege3 | |- ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-frege2 | |- ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) |
|
| 2 | ax-frege1 | |- ( ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ps ) -> ( ( ch -> ( ph -> ps ) ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) ) ) |