Theorem rlimrel 13316

Description: The limit relation is a relation. (Contributed by Mario Carneiro, 24-Sep-2014.)

Assertion

Ref	Expression
rlimrel

Proof of Theorem rlimrel

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-rlim 13312	. 2
2	1	relopabi 5133	1

Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  A.wral 2807  E.wrex 2808   class class class wbr 4452  domcdm 5004  Relwrel 5009  `cfv 5593  (class class class)co 6296  cpm 7440  cc 9511  cr 9512  clt 9649  cle 9650  cmin 9828  crp 11249  cabs 13067  crli 13308

This theorem is referenced by:  rlim  13318  rlimpm  13323  rlimdm  13374  caucvgrlem2  13497  caucvgr  13498  rlimdmafv  32262

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011  df-rlim 13312