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Theorem rb-ax2 1833
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 pm1.4 887 . . . 4 ((𝜑𝜓) → (𝜓𝜑))
21con3i 151 . . 3 (¬ (𝜓𝜑) → ¬ (𝜑𝜓))
32con1i 146 . 2 (¬ ¬ (𝜑𝜓) → (𝜓𝜑))
43orri 880 1 (¬ (𝜑𝜓) ∨ (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:  rblem1  1837  rblem2  1838  rblem3  1839  rblem4  1840  rblem5  1841  rblem6  1842  re2luk1  1845  re2luk2  1846  re2luk3  1847
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