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Theorem lmrel 20323
 Description: The topological space convergence relation is a relation. (Contributed by NM, 7-Dec-2006.) (Revised by Mario Carneiro, 14-Nov-2013.)
Assertion
Ref Expression
lmrel

Proof of Theorem lmrel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lm 20322 . 2
21relmptopab 6536 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 1007   wcel 1904  wral 2756  wrex 2757  cuni 4190   crn 4840   cres 4841   wrel 4844  wf 5585  cfv 5589  (class class class)co 6308   cpm 7491  cc 9555  cuz 11182  ctop 19994  clm 20319 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pow 4579  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-mpt 4456  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-res 4851  df-ima 4852  df-iota 5553  df-fun 5591  df-fv 5597  df-lm 20322 This theorem is referenced by:  lmfun  20474  cmetcaulem  22336  lmle  22349  heibor1lem  32205  rrncmslem  32228
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