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Theorem luk-3 1579
Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luk-3 (𝜑 → (¬ 𝜑𝜓))

Proof of Theorem luk-3
StepHypRef Expression
1 merlem11 1574 . 2 ((¬ 𝜑 → (¬ 𝜑𝜓)) → (¬ 𝜑𝜓))
2 merlem1 1564 . 2 (((¬ 𝜑 → (¬ 𝜑𝜓)) → (¬ 𝜑𝜓)) → (𝜑 → (¬ 𝜑𝜓)))
31, 2ax-mp 5 1 (𝜑 → (¬ 𝜑𝜓))
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:  luklem2  1581  luklem3  1582
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