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Mirrors > Home > ILE Home > Th. List > brabga | Unicode version |
Description: The law of concretion for a binary relation. (Contributed by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
opelopabga.1 |
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brabga.2 |
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Ref | Expression |
---|---|
brabga |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4019 |
. . 3
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2 | brabga.2 |
. . . 4
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3 | 2 | eleq2i 2256 |
. . 3
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4 | 1, 3 | bitri 184 |
. 2
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5 | opelopabga.1 |
. . 3
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6 | 5 | opelopabga 4281 |
. 2
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7 | 4, 6 | bitrid 192 |
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-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-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 |
This theorem is referenced by: braba 4285 brabg 4287 epelg 4308 brcog 4812 fmptco 5702 ofrfval 6114 clim 11320 isstruct2im 12521 isstruct2r 12522 eqgval 13159 dvdsrd 13441 |
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