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Theorem climrel 10989
 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 10988 . 2
21relopabi 4633 1
 Colors of variables: wff set class Syntax hints:   wa 103   wcel 1463  wral 2391  wrex 2392   class class class wbr 3897   wrel 4512  cfv 5091  (class class class)co 5740  cc 7582   clt 7764   cmin 7897  cz 9005  cuz 9275  crp 9390  cabs 10709   cli 10987 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 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-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099 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 2245  df-ral 2396  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-opab 3958  df-xp 4513  df-rel 4514  df-clim 10988 This theorem is referenced by:  clim  10990  climcl  10991  climi  10996  fclim  11003  climrecl  11033  iserex  11048  climrecvg1n  11057  climcvg1nlem  11058  fsum3cvg3  11105  trirecip  11210
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