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Theorem isptfin 26366
 Description: The statement "is a point-finite cover." (Contributed by Jeff Hankins, 21-Jan-2010.)
Hypothesis
Ref Expression
isptfin.1
Assertion
Ref Expression
isptfin
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem isptfin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 unieq 4016 . . . 4
2 isptfin.1 . . . 4
31, 2syl6eqr 2485 . . 3
4 rabeq 2942 . . . 4
54eleq1d 2501 . . 3
63, 5raleqbidv 2908 . 2
7 df-ptfin 26336 . 2
86, 7elab2g 3076 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2697  crab 2701  cuni 4007  cfn 7101  cptfin 26332 This theorem is referenced by:  finptfin  26368  ptfinfin  26369  lfinpfin  26374 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-uni 4008  df-ptfin 26336
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