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Theorem luklem1 1573
Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 23-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
luklem1.1 (𝜑𝜓)
luklem1.2 (𝜓𝜒)
Assertion
Ref Expression
luklem1 (𝜑𝜒)

Proof of Theorem luklem1
StepHypRef Expression
1 luklem1.2 . 2 (𝜓𝜒)
2 luklem1.1 . . 3 (𝜑𝜓)
3 luk-1 1570 . . 3 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))
42, 3ax-mp 5 . 2 ((𝜓𝜒) → (𝜑𝜒))
51, 4ax-mp 5 1 (𝜑𝜒)
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:  luklem2  1574  luklem3  1575  luklem4  1576  luklem5  1577  luklem6  1578  luklem7  1579  ax2  1582  ax3  1583
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