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Theorem retbwax1 1568
 Description: tbw-ax1 1533 rederived from merco1 1546. This theorem, along with retbwax2 1549, retbwax3 1556, and retbwax4 1548, shows that merco1 1546 with ax-mp 5 can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
retbwax1

Proof of Theorem retbwax1
StepHypRef Expression
1 merco1lem18 1567 . . 3
2 merco1lem16 1565 . . 3
31, 2ax-mp 5 . 2
4 merco1lem15 1564 . . . . . 6
5 merco1lem15 1564 . . . . . 6
64, 5ax-mp 5 . . . . 5
7 merco1lem18 1567 . . . . 5
86, 7ax-mp 5 . . . 4
9 merco1lem14 1563 . . . 4
108, 9ax-mp 5 . . 3
11 merco1lem14 1563 . . . . . 6
12 merco1lem10 1559 . . . . . . . . 9
13 merco1 1546 . . . . . . . . 9
1412, 13ax-mp 5 . . . . . . . 8
15 merco1 1546 . . . . . . . 8
1614, 15ax-mp 5 . . . . . . 7
17 merco1 1546 . . . . . . 7
1816, 17ax-mp 5 . . . . . 6
1911, 18ax-mp 5 . . . . 5
20 merco1lem15 1564 . . . . 5
2119, 20ax-mp 5 . . . 4
22 merco1lem10 1559 . . . . . 6
23 merco1lem9 1558 . . . . . 6
2422, 23ax-mp 5 . . . . 5
25 merco1lem13 1562 . . . . 5
2624, 25ax-mp 5 . . . 4
2721, 26ax-mp 5 . . 3
2810, 27ax-mp 5 . 2
293, 28ax-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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