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Theorem luklem7 1429
 Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
luklem7 ((φ → (ψχ)) → (ψ → (φχ)))

Proof of Theorem luklem7
StepHypRef Expression
1 luk-1 1420 . 2 ((φ → (ψχ)) → (((ψχ) → χ) → (φχ)))
2 luklem5 1427 . . . . 5 (ψ → ((ψχ) → ψ))
3 luk-1 1420 . . . . 5 (((ψχ) → ψ) → ((ψχ) → ((ψχ) → χ)))
42, 3luklem1 1423 . . . 4 (ψ → ((ψχ) → ((ψχ) → χ)))
5 luklem6 1428 . . . 4 (((ψχ) → ((ψχ) → χ)) → ((ψχ) → χ))
64, 5luklem1 1423 . . 3 (ψ → ((ψχ) → χ))
7 luk-1 1420 . . 3 ((ψ → ((ψχ) → χ)) → ((((ψχ) → χ) → (φχ)) → (ψ → (φχ))))
86, 7ax-mp 8 . 2 ((((ψχ) → χ) → (φχ)) → (ψ → (φχ)))
91, 8luklem1 1423 1 ((φ → (ψχ)) → (ψ → (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:  luklem8  1430  ax2  1432
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