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Theorem rb-ax3 1676
Description: The third 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-ax3 𝜑 ∨ (𝜓𝜑))

Proof of Theorem rb-ax3
StepHypRef Expression
1 pm2.46 413 . . 3 (¬ (𝜓𝜑) → ¬ 𝜑)
21con1i 144 . 2 (¬ ¬ 𝜑 → (𝜓𝜑))
32orri 391 1 𝜑 ∨ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 383
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 385
This theorem is referenced by:  rblem2  1680  rblem4  1682  rblem5  1683  rblem6  1684  rblem7  1685  re2luk1  1687  re2luk2  1688  re2luk3  1689
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