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Theorem tbwlem2 1539
 Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
tbwlem2

Proof of Theorem tbwlem2
StepHypRef Expression
1 tbw-ax4 1536 . . . . 5
2 tbw-ax1 1533 . . . . . 6
3 tbwlem1 1538 . . . . . 6
42, 3ax-mp 5 . . . . 5
51, 4ax-mp 5 . . . 4
6 tbwlem1 1538 . . . 4
75, 6ax-mp 5 . . 3
8 tbw-ax1 1533 . . 3
9 tbw-ax1 1533 . . 3
107, 8, 9mpsyl 63 . 2
11 tbw-ax1 1533 . 2
1210, 11tbwsyl 1537 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wfal 1400 This theorem is referenced by:  tbwlem4  1541 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 185  df-tru 1398  df-fal 1401
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