Metamath Proof Explorer


Theorem frege45

Description: Deduce pm2.6 from con1 . Proposition 45 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege45 ¬ φ ψ ¬ ψ φ ¬ φ ψ φ ψ ψ

Proof

Step Hyp Ref Expression
1 frege44 ¬ ψ φ φ ψ ψ
2 frege5 ¬ ψ φ φ ψ ψ ¬ φ ψ ¬ ψ φ ¬ φ ψ φ ψ ψ
3 1 2 ax-mp ¬ φ ψ ¬ ψ φ ¬ φ ψ φ ψ ψ