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 ( ( 𝜑𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 bicom1 ( ( 𝜑𝜓 ) → ( 𝜓𝜑 ) )
2 frege54cor0a ( ( 𝜓𝜑 ) ↔ if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )
3 1 2 sylib ( ( 𝜑𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )