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Theorem elexi 2564
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 2563 . 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 1393   _Vcvv 2554
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2556
This theorem is referenced by:  onunisuci  4165  ordsoexmid  4280  fnoei  6019  oeiexg  6020  endisj  6285  indpi  6421  prarloclemarch2  6498  prarloclemlt  6572  opelreal  6885  elreal  6886  elreal2  6888  eqresr  6893  c0ex  7002  1ex  7003  2ex  7963  3ex  7967  pnfex  8660  elxr  8663
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