Metamath Proof Explorer


Theorem frege55cor1a

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

Ref Expression
Assertion frege55cor1a ( ( 𝜑𝜓 ) → ( 𝜓𝜑 ) )

Proof

Step Hyp Ref Expression
1 frege55a ( ( 𝜑𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) )
2 frege55lem1a ( ( ( 𝜑𝜓 ) → if- ( 𝜓 , 𝜑 , ¬ 𝜑 ) ) → ( ( 𝜑𝜓 ) → ( 𝜓𝜑 ) ) )
3 1 2 ax-mp ( ( 𝜑𝜓 ) → ( 𝜓𝜑 ) )