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Theorem merlem6 1612
Description: Step 12 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
merlem6 (𝜒 → (((𝜓𝜒) → 𝜑) → (𝜃𝜑)))

Proof of Theorem merlem6
StepHypRef Expression
1 merlem4 1610 . 2 ((𝜓𝜒) → (((𝜓𝜒) → 𝜑) → (𝜃𝜑)))
2 merlem3 1609 . 2 (((𝜓𝜒) → (((𝜓𝜒) → 𝜑) → (𝜃𝜑))) → (𝜒 → (((𝜓𝜒) → 𝜑) → (𝜃𝜑))))
31, 2ax-mp 5 1 (𝜒 → (((𝜓𝜒) → 𝜑) → (𝜃𝜑)))
Colors of variables: wff setvar class
Syntax hints:  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:  merlem7  1613  merlem9  1615  merlem13  1619
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