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Theorem re1tbw4 1581
 Description: tbw-ax4 1536 rederived from merco2 1569. This theorem, along with re1tbw1 1578, re1tbw2 1579, and re1tbw3 1580, shows that merco2 1569, along with ax-mp 5, can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1tbw4

Proof of Theorem re1tbw4
StepHypRef Expression
1 re1tbw3 1580 . . 3
2 re1tbw2 1579 . . . 4
3 re1tbw1 1578 . . . 4
42, 3ax-mp 5 . . 3
51, 4ax-mp 5 . 2
6 re1tbw3 1580 . . . . 5
7 re1tbw2 1579 . . . . . 6
8 re1tbw1 1578 . . . . . 6
97, 8ax-mp 5 . . . . 5
106, 9ax-mp 5 . . . 4
11 mercolem3 1572 . . . . 5
12 merco2 1569 . . . . 5
1311, 12ax-mp 5 . . . 4
1410, 13ax-mp 5 . . 3
155, 14ax-mp 5 . 2
165, 15ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wfal 1400 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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