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Theorem elom 4850
 Description: Membership in omega. The left conjunct can be eliminated if we assume the Axiom of Infinity; see elom3 7605. (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 2498 . . . 4
21imbi2d 309 . . 3
32albidv 1636 . 2
4 df-om 4848 . 2
53, 4elrab2 3096 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wcel 1726  con0 4583   wlim 4584  com 4847 This theorem is referenced by:  limomss  4852  ordom  4856  nnlim  4860  limom  4862  elom3  7605  dfom5b  25759 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-om 4848
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