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Theorem eldm2 4533
 Description: Membership in a domain. Theorem 4 of [Suppes] p. 59. (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
eldm.1
Assertion
Ref Expression
eldm2
Distinct variable groups:   ,   ,

Proof of Theorem eldm2
StepHypRef Expression
1 eldm.1 . 2
2 eldm2g 4531 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wb 98  wex 1381   wcel 1393  cvv 2557  cop 3378   cdm 4345 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-dm 4355 This theorem is referenced by:  dmss  4534  opeldm  4538  dmin  4543  dmiun  4544  dmuni  4545  dm0  4549  reldm0  4553  dmrnssfld  4595  dmcoss  4601  dmcosseq  4603  dmres  4632  iss  4654  dmxpss  4753  dmsnopg  4792  relssdmrn  4841  funssres  4942  fun11iun  5147  tfrlemibxssdm  5941
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