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Theorem retbwax1 1509
 Description: tbw-ax1 1474 rederived from merco1 1487. This theorem, along with retbwax2 1490, retbwax3 1497, and retbwax4 1489, shows that merco1 1487 with ax-mp 8 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 1508 . . 3
2 merco1lem16 1506 . . 3
31, 2ax-mp 8 . 2
4 merco1lem15 1505 . . . . . 6
5 merco1lem15 1505 . . . . . 6
64, 5ax-mp 8 . . . . 5
7 merco1lem18 1508 . . . . 5
86, 7ax-mp 8 . . . 4
9 merco1lem14 1504 . . . 4
108, 9ax-mp 8 . . 3
11 merco1lem14 1504 . . . . . 6
12 merco1lem10 1500 . . . . . . . . 9
13 merco1 1487 . . . . . . . . 9
1412, 13ax-mp 8 . . . . . . . 8
15 merco1 1487 . . . . . . . 8
1614, 15ax-mp 8 . . . . . . 7
17 merco1 1487 . . . . . . 7
1816, 17ax-mp 8 . . . . . 6
1911, 18ax-mp 8 . . . . 5
20 merco1lem15 1505 . . . . 5
2119, 20ax-mp 8 . . . 4
22 merco1lem10 1500 . . . . . 6
23 merco1lem9 1499 . . . . . 6
2422, 23ax-mp 8 . . . . 5
25 merco1lem13 1503 . . . . 5
2624, 25ax-mp 8 . . . 4
2721, 26ax-mp 8 . . 3
2810, 27ax-mp 8 . 2
293, 28ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   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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