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Theorem ptfinfin 26380
 Description: A point covered by a point-finite cover is only covered by finitely many elements. (Contributed by Jeff Hankins, 21-Jan-2010.)
Hypothesis
Ref Expression
ptfinfin.1
Assertion
Ref Expression
ptfinfin
Distinct variable groups:   ,   ,   ,

Proof of Theorem ptfinfin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ptfinfin.1 . . . . 5
21isptfin 26377 . . . 4
32ibi 234 . . 3
4 eleq1 2498 . . . . . 6
54rabbidv 2950 . . . . 5
65eleq1d 2504 . . . 4
76rspccv 3051 . . 3
83, 7syl 16 . 2
98imp 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wral 2707  crab 2711  cuni 4017  cfn 7111  cptfin 26343 This theorem is referenced by:  locfindis  26387  comppfsc  26389 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-uni 4018  df-ptfin 26347
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