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Theorem elfvexd 6683
Description: If a function value has a member, then its argument is a set. Deduction form of elfvex 6682. (An artifact of our function value definition.) (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
elfvexd.1 (𝜑𝐴 ∈ (𝐵𝐶))
Assertion
Ref Expression
elfvexd (𝜑𝐶 ∈ V)

Proof of Theorem elfvexd
StepHypRef Expression
1 elfvexd.1 . 2 (𝜑𝐴 ∈ (𝐵𝐶))
2 elfvex 6682 . 2 (𝐴 ∈ (𝐵𝐶) → 𝐶 ∈ V)
31, 2syl 17 1 (𝜑𝐶 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2112  Vcvv 3444  cfv 6328
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-nul 5177  ax-pow 5234
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ral 3114  df-rex 3115  df-v 3446  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-dm 5533  df-iota 6287  df-fv 6336
This theorem is referenced by:  mrieqv2d  16906  mreexmrid  16910  mreexexlem3d  16913  mreexexlem4d  16914  mreexexd  16915  mreexdomd  16916  acsdomd  17787  ismgmn0  17850  telgsumfz  19107  isirred  19449  tgclb  21579  alexsublem  22653  cnextcn  22676  ustssel  22815  fmucnd  22902  trcfilu  22904  cfiluweak  22905  ucnextcn  22914  imasdsf1olem  22984  imasf1oxmet  22986  comet  23124  restmetu  23181  wlkp1lem4  27470  wlkp1lem8  27474  1wlkdlem4  27929  eupth2lem3lem1  28017  eupth2lem3lem2  28018  gsumsubg  30735  lbsdiflsp0  31114  fedgmullem1  31117  mzpcl34  39665  xlimbr  42462  xlimmnfvlem2  42468  xlimpnfvlem2  42472
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