Metamath Proof Explorer

Theorem frege14

Description: Closed form of a deduction based on com3r . Proposition 14 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege14 
|- ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) )

Proof

Step Hyp Ref Expression
1 frege13 
 |-  ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( th -> ( ps -> ( ch -> ta ) ) ) )
2 frege5 
 |-  ( ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( th -> ( ps -> ( ch -> ta ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) )