Theorem elexd 2670

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

Step	Hyp	Ref	Expression
1		elexd.1	. 2 |- ( ph -> A e. V )
2		elex 2668	. 2 |- ( A e. V -> A e. _V )
3	1, 2	syl 14	1 |- ( ph -> A e. _V )

Syntax hints:   -> wi 4   e. wcel 1463   _Vcvv 2657

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 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 2659

This theorem is referenced by:  dmmptd  5211  tfr1onlemsucfn  6191  tfrcllemsucfn  6204  frecrdg  6259  unsnfidcel  6762  fnfi  6777  caseinl  6928  caseinr  6929  acfun  7011  seq3val  10121  seqvalcd  10122  hashennn  10416  lcmval  11587  hashdvds  11739  ennnfonelemp1  11761  isstruct2r  11810  strnfvnd  11819  strfvssn  11821  strslfv2d  11841  setsslid  11849  ressid2  11858  ressval2  11859  istopon  12020  istps  12039  tgclb  12074  restbasg  12177  restco  12183  lmfval  12201  cnfval  12203  cnpfval  12204  cnpval  12206  txcnp  12279  txrest  12284  ismet2  12340  xmetpsmet  12355  mopnval  12428  comet  12485  reldvg  12600