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Theorem rb-ax4 1749
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 pm1.2 899 . . . 4 ((𝜑𝜑) → 𝜑)
21con3i 157 . . 3 𝜑 → ¬ (𝜑𝜑))
32con1i 149 . 2 (¬ ¬ (𝜑𝜑) → 𝜑)
43orri 858 1 (¬ (𝜑𝜑) ∨ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 843
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 208  df-or 844
This theorem is referenced by:  rblem4  1754  rblem5  1755  rblem6  1756  re2luk1  1759  re2luk2  1760  re2luk3  1761
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