MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  luklem3 Structured version   Visualization version   GIF version

Theorem luklem3 1625
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
luklem3 (𝜑 → (((¬ 𝜑𝜓) → 𝜒) → (𝜃𝜒)))

Proof of Theorem luklem3
StepHypRef Expression
1 luk-3 1622 . 2 (𝜑 → (¬ 𝜑 → ¬ 𝜃))
2 luklem2 1624 . 2 ((¬ 𝜑 → ¬ 𝜃) → (((¬ 𝜑𝜓) → 𝜒) → (𝜃𝜒)))
31, 2luklem1 1623 1 (𝜑 → (((¬ 𝜑𝜓) → 𝜒) → (𝜃𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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:  luklem4  1626  luklem5  1627
  Copyright terms: Public domain W3C validator