Theorem ax3 1433

Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem ax3

Step	Hyp	Ref	Expression
1		luklem2 1424	. 2 ⊢ ((¬ φ → ¬ ψ) → (((¬ φ → φ) → φ) → (ψ → φ)))
2		luklem4 1426	. 2 ⊢ ((((¬ φ → φ) → φ) → (ψ → φ)) → (ψ → φ))
3	1, 2	luklem1 1423	1 ⊢ ((¬ φ → ¬ ψ) → (ψ → φ))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by: (None)