Theorem merlem6 1412

Description: Step 12 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.)

Assertion

Ref	Expression
merlem6	⊢ (χ → (((ψ → χ) → φ) → (θ → φ)))

Proof of Theorem merlem6

Step	Hyp	Ref	Expression
1		merlem4 1410	. 2 ⊢ ((ψ → χ) → (((ψ → χ) → φ) → (θ → φ)))
2		merlem3 1409	. 2 ⊢ (((ψ → χ) → (((ψ → χ) → φ) → (θ → φ))) → (χ → (((ψ → χ) → φ) → (θ → φ))))
3	1, 2	ax-mp 5	1 ⊢ (χ → (((ψ → χ) → φ) → (θ → φ)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by:  merlem7  1413  merlem9  1415  merlem13  1419