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Theorem climrel 9801
 Description: The limit relation is a relation. (Contributed by NM, 28-Aug-2005.) (Revised by Mario Carneiro, 31-Jan-2014.)
Assertion
Ref Expression
climrel

Proof of Theorem climrel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-clim 9800 . 2
21relopabi 4463 1
 Colors of variables: wff set class Syntax hints:   wa 97   wcel 1393  wral 2306  wrex 2307   class class class wbr 3764   wrel 4350  cfv 4902  (class class class)co 5512  cc 6887   clt 7060   cmin 7182  cz 8245  cuz 8473  crp 8583  cabs 9595   cli 9799 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819  df-xp 4351  df-rel 4352  df-clim 9800 This theorem is referenced by:  clim  9802  climcl  9803  climi  9808  fclim  9815  climrecl  9844  iiserex  9859  climrecvg1n  9867  climcvg1nlem  9868
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