MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rb-ax4 Structured version   Visualization version   GIF version

Theorem rb-ax4 1678
Description: The fourth of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-ax4 (¬ (𝜑𝜑) ∨ 𝜑)

Proof of Theorem rb-ax4
StepHypRef Expression
1 pm1.2 535 . . . 4 ((𝜑𝜑) → 𝜑)
21con3i 150 . . 3 𝜑 → ¬ (𝜑𝜑))
32con1i 144 . 2 (¬ ¬ (𝜑𝜑) → 𝜑)
43orri 391 1 (¬ (𝜑𝜑) ∨ 𝜑)
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
This theorem is referenced by:  rblem4  1683  rblem5  1684  rblem6  1685  re2luk1  1688  re2luk2  1689  re2luk3  1690
  Copyright terms: Public domain W3C validator