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Mirrors > Home > ILE Home > Th. List > brab | Unicode version |
Description: The law of concretion for a binary relation. (Contributed by NM, 16-Aug-1999.) |
Ref | Expression |
---|---|
opelopab.1 | |
opelopab.2 | |
opelopab.3 | |
opelopab.4 | |
brab.5 |
Ref | Expression |
---|---|
brab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopab.1 | . 2 | |
2 | opelopab.2 | . 2 | |
3 | opelopab.3 | . . 3 | |
4 | opelopab.4 | . . 3 | |
5 | brab.5 | . . 3 | |
6 | 3, 4, 5 | brabg 4024 | . 2 |
7 | 1, 2, 6 | mp2an 416 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wcel 1433 cvv 2601 class class class wbr 3785 copab 3838 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 |
This theorem is referenced by: dftpos4 5901 enq0sym 6622 enq0ref 6623 enq0tr 6624 shftfn 9712 |
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