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Theorem eqvisset 2740
Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2736 and issetri 2739. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset  |-  ( x  =  A  ->  A  e.  _V )

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 2733 . 2  |-  x  e. 
_V
2 eleq1 2233 . 2  |-  ( x  =  A  ->  (
x  e.  _V  <->  A  e.  _V ) )
31, 2mpbii 147 1  |-  ( x  =  A  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1348    e. wcel 2141   _Vcvv 2730
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732
This theorem is referenced by:  elxp5  5099  xpsnen  6799  fival  6947
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