Theorem ax3 671

Description: Standard propositional axiom derived from Lukasiewicz axioms.

Assertion

Ref	Expression
ax3	⊢ ((¬ φ → ¬ ψ) → (ψ → φ))

Proof of Theorem ax3

Step	Hyp	Ref	Expression
1		luklem2 662	. 2 ⊢ ((¬ φ → ¬ ψ) → (((¬ φ → φ) → φ) → (ψ → φ)))
2		luklem4 664	. 2 ⊢ ((((¬ φ → φ) → φ) → (ψ → φ)) → (ψ → φ))
3	1, 2	luklem1 661	1 ⊢ ((¬ φ → ¬ ψ) → (ψ → φ))

Syntax hints:  ¬ wn 1   → wi 2

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

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