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Theorem elexd 2623
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 2621 . 2 (𝐴𝑉𝐴 ∈ V)
31, 2syl 14 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  Vcvv 2612
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2614
This theorem is referenced by:  tfr1onlemsucfn  6037  tfrcllemsucfn  6050  frecrdg  6105  unsnfidcel  6558  fnfi  6571  hashennn  10023  lcmval  10825  hashdvds  10977
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