Metamath Proof Explorer


Theorem merlem12

Description: Step 28 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 merlem12 θ ¬ ¬ χ χ φ φ

Proof

Step Hyp Ref Expression
1 merlem5 χ χ ¬ ¬ χ χ
2 merlem2 χ χ ¬ ¬ χ χ θ ¬ ¬ χ χ
3 1 2 ax-mp θ ¬ ¬ χ χ
4 merlem4 θ ¬ ¬ χ χ θ ¬ ¬ χ χ φ θ ¬ ¬ χ χ φ φ
5 3 4 ax-mp θ ¬ ¬ χ χ φ θ ¬ ¬ χ χ φ φ
6 merlem11 θ ¬ ¬ χ χ φ θ ¬ ¬ χ χ φ φ θ ¬ ¬ χ χ φ φ
7 5 6 ax-mp θ ¬ ¬ χ χ φ φ