Theorem luk-3 660

Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom.

Assertion

Ref	Expression
luk-3	⊢ (φ → (¬ φ → ψ))

Proof of Theorem luk-3

Step	Hyp	Ref	Expression
1		merlem11 655	. 2 ⊢ ((¬ φ → (¬ φ → ψ)) → (¬ φ → ψ))
2		merlem1 645	. 2 ⊢ (((¬ φ → (¬ φ → ψ)) → (¬ φ → ψ)) → (φ → (¬ φ → ψ)))
3	1, 2	ax-mp 6	1 ⊢ (φ → (¬ φ → ψ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  luklem2 662  luklem3 663

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

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