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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 982 |
. . 3
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2 | anabs1 572 |
. . 3
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3 | anidm 396 |
. . 3
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4 | 1, 2, 3 | 3bitrri 207 |
. 2
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5 | pocl 4321 |
. . . 4
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6 | 5 | imp 124 |
. . 3
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7 | 6 | simpld 112 |
. 2
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8 | 4, 7 | sylan2b 287 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-po 4314 |
This theorem is referenced by: po2nr 4327 pofun 4330 sonr 4335 poirr2 5039 poxp 6256 swoer 6586 tridc 6926 fimax2gtrilemstep 6927 |
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