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Mirrors > Home > ILE Home > Th. List > breldmg | Unicode version |
Description: Membership of first of a binary relation in a domain. (Contributed by NM, 21-Mar-2007.) |
Ref | Expression |
---|---|
breldmg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 3903 | . . . . 5 | |
2 | 1 | spcegv 2748 | . . . 4 |
3 | 2 | imp 123 | . . 3 |
4 | 3 | 3adant1 984 | . 2 |
5 | eldmg 4704 | . . 3 | |
6 | 5 | 3ad2ant1 987 | . 2 |
7 | 4, 6 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 947 wex 1453 wcel 1465 class class class wbr 3899 cdm 4509 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-dm 4519 |
This theorem is referenced by: brelrng 4740 releldm 4744 brtposg 6119 shftfvalg 10558 shftfval 10561 geolim2 11249 geoisum1c 11257 eftlub 11323 eflegeo 11335 dvcj 12769 dvrecap 12773 dvef 12783 trilpolemisumle 13158 trilpolemeq1 13160 |
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