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Theorem rbsyl 1721
Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
rbsyl.1 𝜓𝜒)
rbsyl.2 (𝜑𝜓)
Assertion
Ref Expression
rbsyl (𝜑𝜒)

Proof of Theorem rbsyl
StepHypRef Expression
1 rbsyl.2 . 2 (𝜑𝜓)
2 rbsyl.1 . . 3 𝜓𝜒)
3 rb-ax1 1717 . . 3 (¬ (¬ 𝜓𝜒) ∨ (¬ (𝜑𝜓) ∨ (𝜑𝜒)))
42, 3anmp 1716 . 2 (¬ (𝜑𝜓) ∨ (𝜑𝜒))
51, 4anmp 1716 1 (𝜑𝜒)
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  df-an 385
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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