Theorem merlem2 646

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

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

Proof of Theorem merlem2

Step	Hyp	Ref	Expression
1		merlem1 645	. 2 ⊢ ((((χ → χ) → (¬ φ → ¬ θ)) → φ) → (φ → φ))
2		meredith 644	. 2 ⊢ (((((χ → χ) → (¬ φ → ¬ θ)) → φ) → (φ → φ)) → (((φ → φ) → χ) → (θ → χ)))
3	1, 2	ax-mp 6	1 ⊢ (((φ → φ) → χ) → (θ → χ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  merlem3 647  merlem12 656

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

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