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Theorem elexd 2621
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  |-  ( ph  ->  A  e.  V )
Assertion
Ref Expression
elexd  |-  ( ph  ->  A  e.  _V )

Proof of Theorem elexd
StepHypRef Expression
1 elexd.1 . 2  |-  ( ph  ->  A  e.  V )
2 elex 2619 . 2  |-  ( A  e.  V  ->  A  e.  _V )
31, 2syl 14 1  |-  ( ph  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   _Vcvv 2610
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 2612
This theorem is referenced by:  tfr1onlemsucfn  6009  tfrcllemsucfn  6022  frecrdg  6077  unsnfidcel  6465  fnfi  6478  hashennn  9856  lcmval  10652  hashdvds  10804
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