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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 11187 | . 2 | |
2 | 1 | relopabi 4714 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 2128 wral 2435 wrex 2436 class class class wbr 3967 wrel 4593 cfv 5172 (class class class)co 5826 cc 7732 clt 7914 cmin 8050 cz 9172 cuz 9444 crp 9566 cabs 10908 cli 11186 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-opab 4028 df-xp 4594 df-rel 4595 df-clim 11187 |
This theorem is referenced by: clim 11189 climcl 11190 climi 11195 fclim 11202 climrecl 11232 iserex 11247 climrecvg1n 11256 climcvg1nlem 11257 fsum3cvg3 11304 trirecip 11409 ntrivcvgap0 11457 |
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