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Theorem rb-ax2 1518
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 (¬ (φ ψ) (ψ φ))

Proof of Theorem rb-ax2
StepHypRef Expression
1 pm1.4 375 . . . 4 ((φ ψ) → (ψ φ))
21con3i 127 . . 3 (¬ (ψ φ) → ¬ (φ ψ))
32con1i 121 . 2 (¬ ¬ (φ ψ) → (ψ φ))
43orri 365 1 (¬ (φ ψ) (ψ 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:  rblem1  1522  rblem2  1523  rblem3  1524  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532
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