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Theorem flimelbas 20975
 Description: A limit point of a filter belongs to its base set. (Contributed by Jeff Hankins, 4-Sep-2009.) (Revised by Mario Carneiro, 9-Apr-2015.)
Hypothesis
Ref Expression
flimuni.1
Assertion
Ref Expression
flimelbas

Proof of Theorem flimelbas
StepHypRef Expression
1 flimuni.1 . . . 4
21elflim2 20971 . . 3
32simprbi 466 . 2
43simpld 461 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   w3a 983   wceq 1438   wcel 1869   wss 3437  cpw 3980  csn 3997  cuni 4217   crn 4852  cfv 5599  (class class class)co 6303  ctop 19909  cnei 20105  cfil 20852   cflim 20941 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-8 1871  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pow 4600  ax-pr 4658 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-sbc 3301  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-pw 3982  df-sn 3998  df-pr 4000  df-op 4004  df-uni 4218  df-br 4422  df-opab 4481  df-id 4766  df-xp 4857  df-rel 4858  df-cnv 4859  df-co 4860  df-dm 4861  df-iota 5563  df-fun 5601  df-fv 5607  df-ov 6306  df-oprab 6307  df-mpt2 6308  df-top 19913  df-flim 20946 This theorem is referenced by:  flimfil  20976  flimss2  20979  flimss1  20980  flimclsi  20985  hausflimi  20987  flimsncls  20993  cnpflfi  21006  cnflf  21009  cnflf2  21010  flimcfil  22275
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