Description: A closed form of syl6 . The first antecedent is used to replace the consequent of the second antecedent. Proposition 7 of Frege1879 p. 34. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege7 | |- ( ( ph -> ps ) -> ( ( ch -> ( th -> ph ) ) -> ( ch -> ( th -> ps ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege5 | |- ( ( ph -> ps ) -> ( ( th -> ph ) -> ( th -> ps ) ) ) |
|
| 2 | frege6 | |- ( ( ( ph -> ps ) -> ( ( th -> ph ) -> ( th -> ps ) ) ) -> ( ( ph -> ps ) -> ( ( ch -> ( th -> ph ) ) -> ( ch -> ( th -> ps ) ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ps ) -> ( ( ch -> ( th -> ph ) ) -> ( ch -> ( th -> ps ) ) ) ) |