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Theorem merlem4 1410
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 ax-meredith 1406 . 2 (((((φφ) → (¬ θ → ¬ θ)) → θ) → τ) → ((τφ) → (θφ)))
2 merlem3 1409 . 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-meredith 1406
This theorem is referenced by:  merlem5  1411  merlem6  1412  merlem7  1413  merlem12  1418  luk-2  1421
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