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Theorem merlem12 1418
 Description: Step 28 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
merlem12 (((θ → (¬ ¬ χχ)) → φ) → φ)

Proof of Theorem merlem12
StepHypRef Expression
1 merlem5 1411 . . . 4 ((χχ) → (¬ ¬ χχ))
2 merlem2 1408 . . . 4 (((χχ) → (¬ ¬ χχ)) → (θ → (¬ ¬ χχ)))
31, 2ax-mp 8 . . 3 (θ → (¬ ¬ χχ))
4 merlem4 1410 . . 3 ((θ → (¬ ¬ χχ)) → (((θ → (¬ ¬ χχ)) → φ) → (((θ → (¬ ¬ χχ)) → φ) → φ)))
53, 4ax-mp 8 . 2 (((θ → (¬ ¬ χχ)) → φ) → (((θ → (¬ ¬ χχ)) → φ) → φ))
6 merlem11 1417 . 2 ((((θ → (¬ ¬ χχ)) → φ) → (((θ → (¬ ¬ χχ)) → φ) → φ)) → (((θ → (¬ ¬ χχ)) → φ) → φ))
75, 6ax-mp 8 1 (((θ → (¬ ¬ χχ)) → φ) → φ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4 This theorem was proved from axioms:  ax-mp 8  ax-meredith 1406 This theorem is referenced by:  merlem13  1419
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