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Mirrors > Home > NFE Home > Th. List > re1luk3 | Unicode version |
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.) |
Ref | Expression |
---|---|
re1luk3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tbw-negdf 1464 |
. . 3
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2 | tbwlem5 1474 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | tbw-ax4 1468 |
. . . 4
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5 | tbw-ax1 1465 |
. . . . 5
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6 | tbwlem1 1470 |
. . . . 5
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7 | 5, 6 | ax-mp 5 |
. . . 4
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8 | 4, 7 | ax-mp 5 |
. . 3
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9 | tbwlem1 1470 |
. . 3
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10 | 8, 9 | ax-mp 5 |
. 2
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11 | tbw-ax1 1465 |
. 2
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12 | 3, 10, 11 | mpsyl 59 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
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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