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Theorem isfin6 8701
 Description: Definition of a VI-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin6

Proof of Theorem isfin6
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-fin6 8691 . . 3
21eleq2i 2535 . 2
3 relsdom 7543 . . . . 5
43brrelexi 5045 . . . 4
53brrelexi 5045 . . . 4
64, 5jaoi 379 . . 3
7 breq1 4455 . . . 4
8 id 22 . . . . 5
98sqxpeqd 5030 . . . . 5
108, 9breq12d 4465 . . . 4
117, 10orbi12d 709 . . 3
126, 11elab3 3253 . 2
132, 12bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  {cab 2442   cvv 3109   class class class wbr 4452  X.cxp 5002   c2o 7143   csdm 7535   cfin6 8684 This theorem is referenced by:  fin56  8794  fin67  8796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-dom 7538  df-sdom 7539  df-fin6 8691
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