Metamath Proof Explorer

Theorem frege13

Description: A closed form of com3r . Proposition 13 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege13 
|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) )

Proof

Step Hyp Ref Expression
1 frege12 
 |-  ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )
2 frege12 
 |-  ( ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ch -> ( ph -> ( ps -> th ) ) ) )