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Theorem rblem3 1524
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 (¬ (χ φ) ((χ ψ) φ))

Proof of Theorem rblem3
StepHypRef Expression
1 rb-ax2 1518 . 2 (¬ (φ (χ ψ)) ((χ ψ) φ))
2 rblem2 1523 . . 3 (¬ (φ χ) (φ (χ ψ)))
3 rb-ax2 1518 . . 3 (¬ (χ φ) (φ χ))
42, 3rbsyl 1521 . 2 (¬ (χ φ) (φ (χ ψ)))
51, 4rbsyl 1521 1 (¬ (χ φ) ((χ 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  df-an 360
This theorem is referenced by:  rblem6  1527
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