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Theorem eldmg 4558
 Description: Domain membership. Theorem 4 of [Suppes] p. 59. (Contributed by Mario Carneiro, 9-Jul-2014.)
Assertion
Ref Expression
eldmg
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eldmg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq1 3796 . . 3
21exbidv 1747 . 2
3 df-dm 4381 . 2
42, 3elab2g 2741 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wex 1422   wcel 1434   class class class wbr 3793   cdm 4371 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-dm 4381 This theorem is referenced by:  eldm2g  4559  eldm  4560  breldmg  4569  releldmb  4599  funeu  4956  fneu  5034  ndmfvg  5236  erref  6192  ecdmn0m  6214  shftdm  9848
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