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Theorem elexi 2584
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
StepHypRef Expression
1 elisseti.1 . 2  |-  A  e.  B
2 elex 2583 . 2  |-  ( A  e.  B  ->  A  e.  _V )
31, 2ax-mp 7 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1409   _Vcvv 2574
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576
This theorem is referenced by:  onunisuci  4197  ordsoexmid  4314  fnoei  6063  oeiexg  6064  endisj  6329  indpi  6498  prarloclemarch2  6575  prarloclemlt  6649  opelreal  6962  elreal  6963  elreal2  6965  eqresr  6970  c0ex  7079  1ex  7080  2ex  8062  3ex  8066  pnfex  8794  elxr  8797
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