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Theorem re1luk3 1477
 Description: luk-3 1422 derived from the Tarski-Bernays-Wajsberg axioms. This theorem, along with re1luk1 1475 and re1luk2 1476 proves that tbw-ax1 1465, tbw-ax2 1466, tbw-ax3 1467, and tbw-ax4 1468, with ax-mp 5 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 1464 . . 3
2 tbwlem5 1474 . . 3
31, 2ax-mp 5 . 2
4 tbw-ax4 1468 . . . 4
5 tbw-ax1 1465 . . . . 5
6 tbwlem1 1470 . . . . 5
75, 6ax-mp 5 . . . 4
84, 7ax-mp 5 . . 3
9 tbwlem1 1470 . . 3
108, 9ax-mp 5 . 2
11 tbw-ax1 1465 . 2
123, 10, 11mpsyl 59 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wfal 1317 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-tru 1319  df-fal 1320 This theorem is referenced by: (None)
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