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Theorem elexd 2671
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 2669 . 2 (𝐴𝑉𝐴 ∈ V)
31, 2syl 14 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  Vcvv 2658
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-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-v 2660
This theorem is referenced by:  dmmptd  5221  tfr1onlemsucfn  6203  tfrcllemsucfn  6216  frecrdg  6271  unsnfidcel  6775  fnfi  6791  caseinl  6942  caseinr  6943  acfun  7027  seq3val  10182  seqvalcd  10183  hashennn  10477  lcmval  11651  hashdvds  11803  ennnfonelemp1  11825  isstruct2r  11876  strnfvnd  11885  strfvssn  11887  strslfv2d  11907  setsslid  11915  ressid2  11924  ressval2  11925  istopon  12086  istps  12105  tgclb  12140  restbasg  12243  restco  12249  lmfval  12267  cnfval  12269  cnpfval  12270  cnpval  12273  txcnp  12346  txrest  12351  ismet2  12429  xmetpsmet  12444  mopnval  12517  comet  12574  reldvg  12723  dvmptclx  12755
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