Theorem elexi 2764

Description: If a class is a member of another class, it is a set. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
elisseti.1	|- A e. B

Assertion

Ref	Expression
elexi	|- A e. _V

Proof of Theorem elexi

Step	Hyp	Ref	Expression
1		elisseti.1	. 2 |- A e. B
2		elex 2763	. 2 |- ( A e. B -> A e. _V )
3	1, 2	ax-mp 5	1 |- A e. _V

Syntax hints:   e. wcel 2160   _Vcvv 2752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-v 2754

This theorem is referenced by:  elpwi2  4176  onunisuci  4450  ordsoexmid  4579  1oex  6449  fnoei  6477  oeiexg  6478  endisj  6850  unfiexmid  6946  snexxph  6979  djuex  7072  0ct  7136  nninfex  7150  infnninfOLD  7153  nnnninf  7154  ctssexmid  7178  nninfdcinf  7199  nninfwlporlem  7201  nninfwlpoimlemg  7203  pm54.43  7219  pw1ne3  7259  3nsssucpw1  7265  2omotaplemst  7287  prarloclemarch2  7448  opelreal  7856  elreal  7857  elreal2  7859  eqresr  7865  c0ex  7981  1ex  7982  pnfex  8041  sup3exmid  8944  2ex  9021  3ex  9025  elxr  9806  setsslid  12563  setsslnid  12564  prdsex  12774  rmodislmod  13667  fnpsr  13945  lgsdir2lem3  14892  subctctexmid  15212  0nninf  15215  nninffeq  15231