Metamath Proof Explorer


Theorem ax2

Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion ax2 φ ψ χ φ ψ φ χ

Proof

Step Hyp Ref Expression
1 luklem7 φ ψ χ ψ φ χ
2 luklem8 ψ φ χ φ ψ φ φ χ
3 luklem6 φ φ χ φ χ
4 luklem8 φ φ χ φ χ φ ψ φ φ χ φ ψ φ χ
5 3 4 ax-mp φ ψ φ φ χ φ ψ φ χ
6 2 5 luklem1 ψ φ χ φ ψ φ χ
7 1 6 luklem1 φ ψ χ φ ψ φ χ