Metamath Proof Explorer

Theorem frege22

Description: A closed form of com45 . Proposition 22 of Frege1879 p. 41. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege22 
|- ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) )

Proof

Step Hyp Ref Expression
1 frege16 
 |-  ( ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) )
2 frege5 
 |-  ( ( ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) )