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Mirrors > Home > ILE Home > Th. List > climrel | Unicode version |
Description: The limit relation is a relation. (Contributed by NM, 28-Aug-2005.) (Revised by Mario Carneiro, 31-Jan-2014.) |
Ref | Expression |
---|---|
climrel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clim 11048 | . 2 | |
2 | 1 | relopabi 4665 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 1480 wral 2416 wrex 2417 class class class wbr 3929 wrel 4544 cfv 5123 (class class class)co 5774 cc 7618 clt 7800 cmin 7933 cz 9054 cuz 9326 crp 9441 cabs 10769 cli 11047 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 df-rel 4546 df-clim 11048 |
This theorem is referenced by: clim 11050 climcl 11051 climi 11056 fclim 11063 climrecl 11093 iserex 11108 climrecvg1n 11117 climcvg1nlem 11118 fsum3cvg3 11165 trirecip 11270 ntrivcvgap0 11318 |
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