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Theorem dmex 4775
Description: The domain of a set is a set. Corollary 6.8(2) of [TakeutiZaring] p. 26. (Contributed by NM, 7-Jul-2008.)
Hypothesis
Ref Expression
dmex.1 𝐴 ∈ V
Assertion
Ref Expression
dmex dom 𝐴 ∈ V

Proof of Theorem dmex
StepHypRef Expression
1 dmex.1 . 2 𝐴 ∈ V
2 dmexg 4773 . 2 (𝐴 ∈ V → dom 𝐴 ∈ V)
31, 2ax-mp 5 1 dom 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1465  Vcvv 2660  dom cdm 4509
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-13 1476  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068  ax-pr 4101  ax-un 4325
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-opab 3960  df-cnv 4517  df-dm 4519  df-rn 4520
This theorem is referenced by:  ofmres  6002  fo1st  6023  tfrlem8  6183  rdgtfr  6239  rdgruledefgg  6240  rdgon  6251  mapprc  6514  ixpprc  6581  ixpssmap2g  6589  ixpssmapg  6590  bren  6609  brdomg  6610  fundmen  6668  xpassen  6692  mapen  6708  ssenen  6713  hashfacen  10547  shftfval  10561
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