Theorem merlem8 652

Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

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

Proof of Theorem merlem8

Step	Hyp	Ref	Expression
1		meredith 644	. 2 ⊢ (((((φ → φ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φ → φ) → (φ → φ)))
2		merlem7 651	. 2 ⊢ ((((((φ → φ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φ → φ) → (φ → φ))) → (((ψ → χ) → θ) → (((χ → τ) → (¬ θ → ¬ ψ)) → θ)))
3	1, 2	ax-mp 6	1 ⊢ (((ψ → χ) → θ) → (((χ → τ) → (¬ θ → ¬ ψ)) → θ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  merlem9 653

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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