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Mirrors > Home > ILE Home > Th. List > breldm | Unicode version |
Description: Membership of first of a binary relation in a domain. (Contributed by NM, 30-Jul-1995.) |
Ref | Expression |
---|---|
opeldm.1 |
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opeldm.2 |
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Ref | Expression |
---|---|
breldm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3896 |
. 2
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2 | opeldm.1 |
. . 3
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3 | opeldm.2 |
. . 3
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4 | 2, 3 | opeldm 4702 |
. 2
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5 | 1, 4 | sylbi 120 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-dm 4509 |
This theorem is referenced by: exse2 4871 funcnv3 5143 dff13 5623 reldmtpos 6104 rntpos 6108 dftpos4 6114 tpostpos 6115 iserd 6409 |
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