MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rblem2 Structured version   Visualization version   GIF version

Theorem rblem2 1681
Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rblem2 (¬ (𝜒𝜑) ∨ (𝜒 ∨ (𝜑𝜓)))

Proof of Theorem rblem2
StepHypRef Expression
1 rb-ax2 1676 . . 3 (¬ (𝜓𝜑) ∨ (𝜑𝜓))
2 rb-ax3 1677 . . 3 𝜑 ∨ (𝜓𝜑))
31, 2rbsyl 1679 . 2 𝜑 ∨ (𝜑𝜓))
4 rb-ax1 1675 . 2 (¬ (¬ 𝜑 ∨ (𝜑𝜓)) ∨ (¬ (𝜒𝜑) ∨ (𝜒 ∨ (𝜑𝜓))))
53, 4anmp 1674 1 (¬ (𝜒𝜑) ∨ (𝜒 ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386
This theorem is referenced by:  rblem3  1682  rblem4  1683  re2luk3  1690
  Copyright terms: Public domain W3C validator