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Theorem locfinbas 26383
 Description: A locally finite cover must cover the base set of its corresponding topological space. (Contributed by Jeff Hankins, 21-Jan-2010.)
Hypotheses
Ref Expression
locfinbas.1
locfinbas.2
Assertion
Ref Expression
locfinbas

Proof of Theorem locfinbas
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 locfinbas.1 . . 3
2 locfinbas.2 . . 3
31, 2islocfin 26378 . 2
43simp2bi 974 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   wne 2601  wral 2707  wrex 2708  crab 2711   cin 3321  c0 3630  cuni 4017  cfv 5456  cfn 7111  ctop 16960  clocfin 26344 This theorem is referenced by:  lfinpfin  26385  locfincmp  26386  locfindis  26387  locfincf  26388 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405  ax-un 4703 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fv 5464  df-top 16965  df-locfin 26348
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