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Theorem merlem8 1571
Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
merlem8 (((𝜓𝜒) → 𝜃) → (((𝜒𝜏) → (¬ 𝜃 → ¬ 𝜓)) → 𝜃))

Proof of Theorem merlem8
StepHypRef Expression
1 meredith 1563 . 2 (((((𝜑𝜑) → (¬ 𝜑 → ¬ 𝜑)) → 𝜑) → 𝜑) → ((𝜑𝜑) → (𝜑𝜑)))
2 merlem7 1570 . 2 ((((((𝜑𝜑) → (¬ 𝜑 → ¬ 𝜑)) → 𝜑) → 𝜑) → ((𝜑𝜑) → (𝜑𝜑))) → (((𝜓𝜒) → 𝜃) → (((𝜒𝜏) → (¬ 𝜃 → ¬ 𝜓)) → 𝜃)))
31, 2ax-mp 5 1 (((𝜓𝜒) → 𝜃) → (((𝜒𝜏) → (¬ 𝜃 → ¬ 𝜓)) → 𝜃))
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:  merlem9  1572
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