Metamath Proof Explorer


Theorem frege46

Description: If ps holds when ph occurs as well as when ph does not occur, then ps holds. If ps or ph occurs and if the occurrences of ph has ps as a necessary consequence, then ps takes place. Identical to pm2.6 . Proposition 46 of Frege1879 p. 48. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege46 ¬φψφψψ

Proof

Step Hyp Ref Expression
1 frege33 ¬φψ¬ψφ
2 frege45 ¬φψ¬ψφ¬φψφψψ
3 1 2 ax-mp ¬φψφψψ