Theorem merlem4 648

Description: Step 8 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem4	⊢ (τ → ((τ → φ) → (θ → φ)))

Proof of Theorem merlem4

Step	Hyp	Ref	Expression
1		meredith 644	. 2 ⊢ (((((φ → φ) → (¬ θ → ¬ θ)) → θ) → τ) → ((τ → φ) → (θ → φ)))
2		merlem3 647	. 2 ⊢ ((((((φ → φ) → (¬ θ → ¬ θ)) → θ) → τ) → ((τ → φ) → (θ → φ))) → (τ → ((τ → φ) → (θ → φ))))
3	1, 2	ax-mp 6	1 ⊢ (τ → ((τ → φ) → (θ → φ)))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  merlem5 649  merlem6 650  merlem7 651  merlem12 656  luk-2 659

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

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