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Theorem eldm2 4732
 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 4730 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104  wex 1468   wcel 1480  cvv 2681  cop 3525   cdm 4534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-dm 4544 This theorem is referenced by:  dmss  4733  opeldm  4737  dmin  4742  dmiun  4743  dmuni  4744  dm0  4748  reldm0  4752  dmrnssfld  4797  dmcoss  4803  dmcosseq  4805  dmres  4835  iss  4860  dmxpss  4964  dmsnopg  5005  relssdmrn  5054  funssres  5160  fun11iun  5381  tfrlemibxssdm  6217  tfr1onlembxssdm  6233  tfrcllembxssdm  6246
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