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Mirrors > Home > ILE Home > Th. List > soirri | Unicode version |
Description: A strict order relation is irreflexive. (Contributed by NM, 10-Feb-1996.) (Revised by Mario Carneiro, 10-May-2013.) |
Ref | Expression |
---|---|
soi.1 |
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soi.2 |
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Ref | Expression |
---|---|
soirri |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. 2
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2 | soi.1 |
. . 3
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3 | soi.2 |
. . . . 5
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4 | 3 | brel 4674 |
. . . 4
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5 | 4 | simpld 112 |
. . 3
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6 | sonr 4313 |
. . 3
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7 | 2, 5, 6 | sylancr 414 |
. 2
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8 | 1, 7 | pm2.65i 639 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-po 4292 df-iso 4293 df-xp 4628 |
This theorem is referenced by: son2lpi 5020 ltsonq 7375 genpdisj 7500 ltposr 7740 axpre-ltirr 7859 |
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