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Theorem elom 6703
Description: Membership in omega. The left conjunct can be eliminated if we assume the Axiom of Infinity; see elom3 8086. (Contributed by NM, 15-May-1994.)
Assertion
Ref Expression
elom
Distinct variable group:   ,

Proof of Theorem elom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2529 . . . 4
21imbi2d 316 . . 3
32albidv 1713 . 2
4 df-om 6701 . 2
53, 4elrab2 3259 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818   con0 4883  Limwlim 4884   com 6700
This theorem is referenced by:  limomss  6705  ordom  6709  nnlim  6713  limom  6715  elom3  8086  dfom5b  29562
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  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-rab 2816  df-v 3111  df-om 6701
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