Description: Closed form for a1d . Deduction introducing an embedded antecedent. Identical to rp-frege24 which was proved without relying on ax-frege8 . Proposition 24 of Frege1879 p. 42. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege24 | |- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-frege1 | |- ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) ) |
|
| 2 | frege12 | |- ( ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) ) -> ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) ) |