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Theorem luklem8 1735
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
luklem8 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))

Proof of Theorem luklem8
StepHypRef Expression
1 luk-1 1725 . 2 ((𝜒𝜑) → ((𝜑𝜓) → (𝜒𝜓)))
2 luklem7 1734 . 2 (((𝜒𝜑) → ((𝜑𝜓) → (𝜒𝜓))) → ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓))))
31, 2ax-mp 5 1 ((𝜑𝜓) → ((𝜒𝜑) → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  ax2  1737
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