NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  rb-ax4 GIF version

Theorem rb-ax4 1520
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 (¬ (φ φ) φ)

Proof of Theorem rb-ax4
StepHypRef Expression
1 pm1.2 499 . . . 4 ((φ φ) → φ)
21con3i 127 . . 3 φ → ¬ (φ φ))
32con1i 121 . 2 (¬ ¬ (φ φ) → φ)
43orri 365 1 (¬ (φ φ) φ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   wo 357
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 177  df-or 359
This theorem is referenced by:  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532
  Copyright terms: Public domain W3C validator