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Theorem luklem5 1732
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luklem5 (𝜑 → (𝜓𝜑))

Proof of Theorem luklem5
StepHypRef Expression
1 luklem3 1730 . 2 (𝜑 → (((¬ 𝜑𝜑) → 𝜑) → (𝜓𝜑)))
2 luklem4 1731 . 2 ((((¬ 𝜑𝜑) → 𝜑) → (𝜓𝜑)) → (𝜓𝜑))
31, 2luklem1 1728 1 (𝜑 → (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:  luklem6  1733  luklem7  1734  ax1  1736
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