MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rb-ax3 Structured version   Visualization version   GIF version

Theorem rb-ax3 1834
Description: The third 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-ax3 𝜑 ∨ (𝜓𝜑))

Proof of Theorem rb-ax3
StepHypRef Expression
1 pm2.46 898 . . 3 (¬ (𝜓𝜑) → ¬ 𝜑)
21con1i 146 . 2 (¬ ¬ 𝜑 → (𝜓𝜑))
32orri 880 1 𝜑 ∨ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 865
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 198  df-or 866
This theorem is referenced by:  rblem2  1838  rblem4  1840  rblem5  1841  rblem6  1842  rblem7  1843  re2luk1  1845  re2luk2  1846  re2luk3  1847
  Copyright terms: Public domain W3C validator