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Theorem rb-ax2 1718
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 pm1.4 400 . . . 4 ((𝜑𝜓) → (𝜓𝜑))
21con3i 150 . . 3 (¬ (𝜓𝜑) → ¬ (𝜑𝜓))
32con1i 144 . 2 (¬ ¬ (𝜑𝜓) → (𝜓𝜑))
43orri 390 1 (¬ (𝜑𝜓) ∨ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 382
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 197  df-or 384
This theorem is referenced by:  rblem1  1722  rblem2  1723  rblem3  1724  rblem4  1725  rblem5  1726  rblem6  1727  re2luk1  1730  re2luk2  1731  re2luk3  1732
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