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 ¬φψ¬ψφ

Proof

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