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 φ ψ if- ψ φ ¬ φ

Proof

Step Hyp Ref Expression
1 bicom1 φ ψ ψ φ
2 frege54cor0a ψ φ if- ψ φ ¬ φ
3 1 2 sylib φ ψ if- ψ φ ¬ φ