Metamath Proof Explorer

Theorem frege55lem2a

Description: Core proof of Proposition 55 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege55lem2a 
|- ( ( ph <-> ps ) -> if- ( ps , ph , -. ph ) )

Proof

Step Hyp Ref Expression
1 bicom1 
 |-  ( ( ph <-> ps ) -> ( ps <-> ph ) )
2 frege54cor0a 
 |-  ( ( ps <-> ph ) <-> if- ( ps , ph , -. ph ) )
3 1 2 sylib 
 |-  ( ( ph <-> ps ) -> if- ( ps , ph , -. ph ) )