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Mirrors > Home > ILE Home > Th. List > poirr | Unicode version |
Description: A partial order relation is irreflexive. (Contributed by NM, 27-Mar-1997.) |
Ref | Expression |
---|---|
poirr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 926 |
. . 3
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2 | anabs1 539 |
. . 3
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3 | anidm 388 |
. . 3
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4 | 1, 2, 3 | 3bitrri 205 |
. 2
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5 | pocl 4130 |
. . . 4
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6 | 5 | imp 122 |
. . 3
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7 | 6 | simpld 110 |
. 2
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8 | 4, 7 | sylan2b 281 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-v 2621 df-un 3003 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 df-po 4123 |
This theorem is referenced by: po2nr 4136 pofun 4139 sonr 4144 poirr2 4824 poxp 5997 swoer 6320 tridc 6615 fimax2gtrilemstep 6616 |
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