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 1756
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 pm2.46 880 . . 3 (¬ (𝜓𝜑) → ¬ 𝜑)
21con1i 149 . 2 (¬ ¬ 𝜑 → (𝜓𝜑))
32orri 859 1 𝜑 ∨ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 844
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 210  df-or 845
This theorem is referenced by:  rblem2  1760  rblem4  1762  rblem5  1763  rblem6  1764  rblem7  1765  re2luk1  1767  re2luk2  1768  re2luk3  1769
  Copyright terms: Public domain W3C validator