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Theorem merlem4 1567
Description: Step 8 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
merlem4 (𝜏 → ((𝜏𝜑) → (𝜃𝜑)))

Proof of Theorem merlem4
StepHypRef Expression
1 meredith 1563 . 2 (((((𝜑𝜑) → (¬ 𝜃 → ¬ 𝜃)) → 𝜃) → 𝜏) → ((𝜏𝜑) → (𝜃𝜑)))
2 merlem3 1566 . 2 ((((((𝜑𝜑) → (¬ 𝜃 → ¬ 𝜃)) → 𝜃) → 𝜏) → ((𝜏𝜑) → (𝜃𝜑))) → (𝜏 → ((𝜏𝜑) → (𝜃𝜑))))
31, 2ax-mp 5 1 (𝜏 → ((𝜏𝜑) → (𝜃𝜑)))
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:  merlem5  1568  merlem6  1569  merlem7  1570  merlem12  1575  luk-2  1578
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