Metamath Proof Explorer


Theorem merlem2

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion merlem2 φ φ χ θ χ

Proof

Step Hyp Ref Expression
1 merlem1 χ χ ¬ φ ¬ θ φ φ φ
2 meredith χ χ ¬ φ ¬ θ φ φ φ φ φ χ θ χ
3 1 2 ax-mp φ φ χ θ χ