Description: Closed form of a syllogism followed by a swap of antecedents. Proposition 18 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege18 | |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ph ) -> ( ps -> ( th -> ch ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege5 | |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ph ) -> ( th -> ( ps -> ch ) ) ) ) |
|
| 2 | frege16 | |- ( ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ph ) -> ( th -> ( ps -> ch ) ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ph ) -> ( ps -> ( th -> ch ) ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ph ) -> ( ps -> ( th -> ch ) ) ) ) |