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Theorem rblem3 1766
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.)
Assertion
Ref Expression
rblem3 (¬ (𝜒𝜑) ∨ ((𝜒𝜓) ∨ 𝜑))

Proof of Theorem rblem3
StepHypRef Expression
1 rb-ax2 1760 . 2 (¬ (𝜑 ∨ (𝜒𝜓)) ∨ ((𝜒𝜓) ∨ 𝜑))
2 rblem2 1765 . . 3 (¬ (𝜑𝜒) ∨ (𝜑 ∨ (𝜒𝜓)))
3 rb-ax2 1760 . . 3 (¬ (𝜒𝜑) ∨ (𝜑𝜒))
42, 3rbsyl 1763 . 2 (¬ (𝜒𝜑) ∨ (𝜑 ∨ (𝜒𝜓)))
51, 4rbsyl 1763 1 (¬ (𝜒𝜑) ∨ ((𝜒𝜓) ∨ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 846
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 210  df-an 400  df-or 847
This theorem is referenced by:  rblem6  1769
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