Metamath Proof Explorer


Theorem frege29

Description: Closed form of con3d . Proposition 29 of Frege1879 p. 43. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege29 φ ψ χ φ ¬ χ ¬ ψ

Proof

Step Hyp Ref Expression
1 ax-frege28 ψ χ ¬ χ ¬ ψ
2 frege5 ψ χ ¬ χ ¬ ψ φ ψ χ φ ¬ χ ¬ ψ
3 1 2 ax-mp φ ψ χ φ ¬ χ ¬ ψ