Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rb-ax2 Structured version   Visualization version   GIF version

Theorem rb-ax2 1755
 Description: The second 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-ax2 (¬ (𝜑𝜓) ∨ (𝜓𝜑))

Proof of Theorem rb-ax2
StepHypRef Expression
1 pm1.4 866 . . . 4 ((𝜑𝜓) → (𝜓𝜑))
21con3i 157 . . 3 (¬ (𝜓𝜑) → ¬ (𝜑𝜓))
32con1i 149 . 2 (¬ ¬ (𝜑𝜓) → (𝜓𝜑))
43orri 859 1 (¬ (𝜑𝜓) ∨ (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:  rblem1  1759  rblem2  1760  rblem3  1761  rblem4  1762  rblem5  1763  rblem6  1764  re2luk1  1767  re2luk2  1768  re2luk3  1769
 Copyright terms: Public domain W3C validator