Metamath Proof Explorer

Theorem frege53aid

Description: Specialization of frege53a . Proposition 53 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege53aid 
|- ( ph -> ( ( ph <-> ps ) -> ps ) )

Proof

Step Hyp Ref Expression
1 frege52aid 
 |-  ( ( ph <-> ps ) -> ( ph -> ps ) )
2 ax-frege8 
 |-  ( ( ( ph <-> ps ) -> ( ph -> ps ) ) -> ( ph -> ( ( ph <-> ps ) -> ps ) ) )
3 1 2 ax-mp 
 |-  ( ph -> ( ( ph <-> ps ) -> ps ) )