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Theorem re1luk3 1486
 Description: luk-3 1431 derived from the Tarski-Bernays-Wajsberg axioms. This theorem, along with re1luk1 1484 and re1luk2 1485 proves that tbw-ax1 1474, tbw-ax2 1475, tbw-ax3 1476, and tbw-ax4 1477, with ax-mp 8 can be used as a complete axiom system for all of propositional calculus. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1luk3

Proof of Theorem re1luk3
StepHypRef Expression
1 tbw-negdf 1473 . . 3
2 tbwlem5 1483 . . 3
31, 2ax-mp 8 . 2
4 tbw-ax4 1477 . . . 4
5 tbw-ax1 1474 . . . . 5
6 tbwlem1 1479 . . . . 5
75, 6ax-mp 8 . . . 4
84, 7ax-mp 8 . . 3
9 tbwlem1 1479 . . 3
108, 9ax-mp 8 . 2
11 tbw-ax1 1474 . 2
123, 10, 11mpsyl 61 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wfal 1326 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-tru 1328  df-fal 1329
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