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Theorem omsson 6704
Description: Omega is a subset of . (Contributed by NM, 13-Jun-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
omsson

Proof of Theorem omsson
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfom2 6702 . 2
2 ssrab2 3584 . 2
31, 2eqsstri 3533 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  {crab 2811  C_wss 3475   con0 4883  Limwlim 4884  succsuc 4885   com 6700
This theorem is referenced by:  limomss  6705  nnon  6706  ordom  6709  omssnlim  6714  nnunifi  7791  unblem1  7792  unblem2  7793  unblem3  7794  unblem4  7795  isfinite2  7798  card2inf  8002  ackbij1lem16  8636  ackbij1lem18  8638  fin23lem26  8726  fin23lem27  8729  isf32lem5  8758  fin1a2lem6  8806  pwfseqlem3  9059  tskinf  9168  grothomex  9228  ltsopi  9287  dmaddpi  9289  dmmulpi  9290  2ndcdisj  19957  omsinds  29299  finminlem  30136
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-8 1820  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  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  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-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-tp 4034  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887  df-lim 4888  df-suc 4889  df-om 6701
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