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Theorem merlem2 1716
Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merlem2 (((𝜑𝜑) → 𝜒) → (𝜃𝜒))

Proof of Theorem merlem2
StepHypRef Expression
1 merlem1 1715 . 2 ((((𝜒𝜒) → (¬ 𝜑 → ¬ 𝜃)) → 𝜑) → (𝜑𝜑))
2 meredith 1714 . 2 (((((𝜒𝜒) → (¬ 𝜑 → ¬ 𝜃)) → 𝜑) → (𝜑𝜑)) → (((𝜑𝜑) → 𝜒) → (𝜃𝜒)))
31, 2ax-mp 5 1 (((𝜑𝜑) → 𝜒) → (𝜃𝜒))
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:  merlem3  1717  merlem12  1726
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