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Mirrors > Home > ILE Home > Th. List > brabg | Unicode version |
Description: The law of concretion for a binary relation. (Contributed by NM, 16-Aug-1999.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
opelopabg.1 | |
opelopabg.2 | |
brabg.5 |
Ref | Expression |
---|---|
brabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopabg.1 | . . 3 | |
2 | opelopabg.2 | . . 3 | |
3 | 1, 2 | sylan9bb 458 | . 2 |
4 | brabg.5 | . 2 | |
5 | 3, 4 | brabga 4242 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1343 wcel 2136 class class class wbr 3982 copab 4042 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-v 2728 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-br 3983 df-opab 4044 |
This theorem is referenced by: brab 4250 opbrop 4683 ideqg 4755 opelcnvg 4784 bren 6713 brdomg 6714 enq0breq 7377 ltresr 7780 ltxrlt 7964 apreap 8485 apreim 8501 shftfibg 10762 shftfib 10765 2shfti 10773 |
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