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Theorem elexd 2632
Description: If a class is a member of another class, it is a set. (Contributed by Glauco Siliprandi, 11-Oct-2020.)
Hypothesis
Ref Expression
elexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
elexd (𝜑𝐴 ∈ V)

Proof of Theorem elexd
StepHypRef Expression
1 elexd.1 . 2 (𝜑𝐴𝑉)
2 elex 2630 . 2 (𝐴𝑉𝐴 ∈ V)
31, 2syl 14 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1438  Vcvv 2619
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-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621
This theorem is referenced by:  tfr1onlemsucfn  6105  tfrcllemsucfn  6118  frecrdg  6173  unsnfidcel  6631  fnfi  6646  seq3val  9874  hashennn  10188  lcmval  11323  hashdvds  11475  isstruct2r  11505  strnfvnd  11515  strfvssn  11518  strslfv2d  11536  setsslid  11544  ressid2  11552  ressval2  11553  istopon  11610
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