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Theorem brdom2 7565
Description: Dominance in terms of strict dominance and equinumerosity. Theorem 22(iv) of [Suppes] p. 97. (Contributed by NM, 17-Jun-1998.)
Assertion
Ref Expression
brdom2

Proof of Theorem brdom2
StepHypRef Expression
1 dfdom2 7561 . . 3
21eleq2i 2535 . 2
3 df-br 4453 . 2
4 df-br 4453 . . . 4
5 df-br 4453 . . . 4
64, 5orbi12i 521 . . 3
7 elun 3644 . . 3
86, 7bitr4i 252 . 2
92, 3, 83bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  e.wcel 1818  u.cun 3473  <.cop 4035   class class class wbr 4452   cen 7533   cdom 7534   csdm 7535
This theorem is referenced by:  bren2  7566  domnsym  7663  modom  7740  carddom2  8379  axcc4dom  8842  entric  8953  entri2  8954  gchor  9026  frgpcyg  18612  iunmbl2  21967  dyadmbl  22009  volmeas  28203  ovoliunnfl  30056  ctbnfien  30752
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-eu 2286  df-mo 2287  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-f1o 5600  df-en 7537  df-dom 7538  df-sdom 7539
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