Metamath Proof Explorer

Theorem frege17

Description: A closed form of com3l . Proposition 17 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege17 
|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) )

Proof

Step Hyp Ref Expression
1 ax-frege8 
 |-  ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ph -> ( ch -> th ) ) ) )
2 frege16 
 |-  ( ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ph -> ( ch -> th ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) )