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Mirrors > Home > NFE Home > Th. List > biass | Unicode version |
Description: Associative law for the biconditional. An axiom of system DS in Vladimir Lifschitz, "On calculational proofs", Annals of Pure and Applied Logic, 113:207-224, 2002, http://www.cs.utexas.edu/users/ai-lab/pub-view.php?PubID=26805. Interestingly, this law was not included in Principia Mathematica but was apparently first noted by Jan Lukasiewicz circa 1923. (Contributed by NM, 8-Jan-2005.) (Proof shortened by Juha Arpiainen, 19-Jan-2006.) (Proof shortened by Wolf Lammen, 21-Sep-2013.) |
Ref | Expression |
---|---|
biass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.501 330 |
. . . 4
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2 | 1 | bibi1d 310 |
. . 3
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3 | pm5.501 330 |
. . 3
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4 | 2, 3 | bitr3d 246 |
. 2
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5 | nbbn 347 |
. . . 4
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6 | nbn2 334 |
. . . . 5
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7 | 6 | bibi1d 310 |
. . . 4
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8 | 5, 7 | syl5bbr 250 |
. . 3
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9 | nbn2 334 |
. . 3
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10 | 8, 9 | bitr3d 246 |
. 2
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11 | 4, 10 | pm2.61i 156 |
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 |
This theorem is referenced by: biluk 899 xorass 1308 had1 1402 |
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