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Theorem ax3 1590
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) → (𝜓𝜑))

Proof of Theorem ax3
StepHypRef Expression
1 luklem2 1581 . 2 ((¬ 𝜑 → ¬ 𝜓) → (((¬ 𝜑𝜑) → 𝜑) → (𝜓𝜑)))
2 luklem4 1583 . 2 ((((¬ 𝜑𝜑) → 𝜑) → (𝜓𝜑)) → (𝜓𝜑))
31, 2luklem1 1580 1 ((¬ 𝜑 → ¬ 𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
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