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Theorem rbsyl 1521
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 ψ χ)
rbsyl.2 (φ ψ)
Assertion
Ref Expression
rbsyl (φ χ)

Proof of Theorem rbsyl
StepHypRef Expression
1 rbsyl.2 . 2 (φ ψ)
2 rbsyl.1 . . 3 ψ χ)
3 rb-ax1 1517 . . 3 (¬ (¬ ψ χ) (¬ (φ ψ) (φ χ)))
42, 3anmp 1516 . 2 (¬ (φ ψ) (φ χ))
51, 4anmp 1516 1 (φ χ)
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:  rblem1  1522  rblem2  1523  rblem3  1524  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532
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