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Theorem isptfin 20543
 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 4209 . . . 4
2 isptfin.1 . . . 4
31, 2syl6eqr 2505 . . 3
4 rabeq 3040 . . . 4
54eleq1d 2515 . . 3
63, 5raleqbidv 3003 . 2
7 df-ptfin 20533 . 2
86, 7elab2g 3189 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wceq 1446   wcel 1889  wral 2739  crab 2743  cuni 4201  cfn 7574  cptfin 20530 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-uni 4202  df-ptfin 20533 This theorem is referenced by:  finptfin  20545  ptfinfin  20546  lfinpfin  20551
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