Metamath Proof Explorer


Theorem frege44

Description: Similar to a commuted pm2.62 . Proposition 44 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege44 ( ( ¬ 𝜑𝜓 ) → ( ( 𝜓𝜑 ) → 𝜑 ) )

Proof

Step Hyp Ref Expression
1 frege43 ( ( ¬ 𝜑𝜑 ) → 𝜑 )
2 frege21 ( ( ( ¬ 𝜑𝜑 ) → 𝜑 ) → ( ( ¬ 𝜑𝜓 ) → ( ( 𝜓𝜑 ) → 𝜑 ) ) )
3 1 2 ax-mp ( ( ¬ 𝜑𝜓 ) → ( ( 𝜓𝜑 ) → 𝜑 ) )