Metamath Proof Explorer


Theorem frege33

Description: If ph or ps takes place, then ps or ph takes place. Identical to con1 . Proposition 33 of Frege1879 p. 44. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege33 ¬ φ ψ ¬ ψ φ

Proof

Step Hyp Ref Expression
1 ax-frege28 ¬ φ ψ ¬ ψ ¬ ¬ φ
2 frege32 ¬ φ ψ ¬ ψ ¬ ¬ φ ¬ φ ψ ¬ ψ φ
3 1 2 ax-mp ¬ φ ψ ¬ ψ φ