Theorem merlem4 930

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 926	. 2 ⊢ (((((φ → φ) → (¬ θ → ¬ θ)) → θ) → τ) → ((τ → φ) → (θ → φ)))
2		merlem3 929	. 2 ⊢ ((((((φ → φ) → (¬ θ → ¬ θ)) → θ) → τ) → ((τ → φ) → (θ → φ))) → (τ → ((τ → φ) → (θ → φ))))
3	1, 2	ax-mp 7	1 ⊢ (τ → ((τ → φ) → (θ → φ)))

Syntax hints:  ¬ wn 2   → wi 3

This theorem is referenced by:  merlem5 931  merlem6 932  merlem7 933  merlem12 938  luk-2 941

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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