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Theorem merlem10 1416
 Description: Step 19 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
merlem10 ((φ → (φψ)) → (θ → (φψ)))

Proof of Theorem merlem10
StepHypRef Expression
1 ax-meredith 1406 . 2 (((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ)))
2 ax-meredith 1406 . . 3 ((((((φψ) → φ) → (¬ φ → ¬ θ)) → φ) → φ) → ((φ → (φψ)) → (θ → (φψ))))
3 merlem9 1415 . . 3 (((((((φψ) → φ) → (¬ φ → ¬ θ)) → φ) → φ) → ((φ → (φψ)) → (θ → (φψ)))) → ((((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ))) → ((φ → (φψ)) → (θ → (φψ)))))
42, 3ax-mp 5 . 2 ((((((φφ) → (¬ φ → ¬ φ)) → φ) → φ) → ((φφ) → (φφ))) → ((φ → (φψ)) → (θ → (φψ))))
51, 4ax-mp 5 1 ((φ → (φψ)) → (θ → (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:  merlem11  1417
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