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Theorem merlem11 1417
 Description: Step 20 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
merlem11 ((φ → (φψ)) → (φψ))

Proof of Theorem merlem11
StepHypRef Expression
1 ax-meredith 1406 . 2 (((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ)))
2 merlem10 1416 . . 3 ((φ → (φψ)) → ((φ → (φψ)) → (φψ)))
3 merlem10 1416 . . 3 (((φ → (φψ)) → ((φ → (φψ)) → (φψ))) → ((((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ))) → ((φ → (φψ)) → (φψ))))
42, 3ax-mp 5 . 2 ((((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ))) → ((φ → (φψ)) → (φψ)))
51, 4ax-mp 5 1 ((φ → (φψ)) → (φψ))
 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:  merlem12  1418  merlem13  1419  luk-2  1421  luk-3  1422
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