Theorem merlem8 1414

Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merlem8	⊢ (((ψ → χ) → θ) → (((χ → τ) → (¬ θ → ¬ ψ)) → θ))

Proof of Theorem merlem8

Step	Hyp	Ref	Expression
1		ax-meredith 1406	. 2 ⊢ (((((φ → φ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φ → φ) → (φ → φ)))
2		merlem7 1413	. 2 ⊢ ((((((φ → φ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φ → φ) → (φ → φ))) → (((ψ → χ) → θ) → (((χ → τ) → (¬ θ → ¬ ψ)) → θ)))
3	1, 2	ax-mp 5	1 ⊢ (((ψ → χ) → θ) → (((χ → τ) → (¬ θ → ¬ ψ)) → θ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-meredith 1406

This theorem is used by:  merlem9  1415