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Theorem eldm2 4476
 Description: Membership in a domain. Theorem 4 of [Suppes] p. 59. (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
eldm.1 A V
Assertion
Ref Expression
eldm2 (A dom ByA, y B)
Distinct variable groups:   y,A   y,B

Proof of Theorem eldm2
StepHypRef Expression
1 eldm.1 . 2 A V
2 eldm2g 4474 . 2 (A V → (A dom ByA, y B))
31, 2ax-mp 7 1 (A dom ByA, y B)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98  ∃wex 1378   ∈ wcel 1390  Vcvv 2551  ⟨cop 3370  dom cdm 4288 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-dm 4298 This theorem is referenced by:  dmss  4477  opeldm  4481  dmin  4486  dmiun  4487  dmuni  4488  dm0  4492  reldm0  4496  dmrnssfld  4538  dmcoss  4544  dmcosseq  4546  dmres  4575  iss  4597  dmxpss  4696  dmsnopg  4735  relssdmrn  4784  funssres  4885  fun11iun  5090  tfrlemibxssdm  5882
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