Theorem merlem2 1408

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.)

Assertion

Ref	Expression
merlem2	⊢ (((φ → φ) → χ) → (θ → χ))

Proof of Theorem merlem2

Step	Hyp	Ref	Expression
1		merlem1 1407	. 2 ⊢ ((((χ → χ) → (¬ φ → ¬ θ)) → φ) → (φ → φ))
2		ax-meredith 1406	. 2 ⊢ (((((χ → χ) → (¬ φ → ¬ θ)) → φ) → (φ → φ)) → (((φ → φ) → χ) → (θ → χ)))
3	1, 2	ax-mp 5	1 ⊢ (((φ → φ) → χ) → (θ → χ))

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by:  merlem3  1409  merlem12  1418