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Theorem ax2 1432
 Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax2 ((φ → (ψχ)) → ((φψ) → (φχ)))

Proof of Theorem ax2
StepHypRef Expression
1 luklem7 1429 . 2 ((φ → (ψχ)) → (ψ → (φχ)))
2 luklem8 1430 . . 3 ((ψ → (φχ)) → ((φψ) → (φ → (φχ))))
3 luklem6 1428 . . . 4 ((φ → (φχ)) → (φχ))
4 luklem8 1430 . . . 4 (((φ → (φχ)) → (φχ)) → (((φψ) → (φ → (φχ))) → ((φψ) → (φχ))))
53, 4ax-mp 8 . . 3 (((φψ) → (φ → (φχ))) → ((φψ) → (φχ)))
62, 5luklem1 1423 . 2 ((ψ → (φχ)) → ((φψ) → (φχ)))
71, 6luklem1 1423 1 ((φ → (ψχ)) → ((φψ) → (φχ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 8  ax-meredith 1406 This theorem is referenced by: (None)
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