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Theorem issetri 2808
Description: A way to say " A is a set" (inference rule). (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
issetri.1  |-  E. x  x  =  A
Assertion
Ref Expression
issetri  |-  A  e. 
_V
Distinct variable group:    x, A

Proof of Theorem issetri
StepHypRef Expression
1 issetri.1 . 2  |-  E. x  x  =  A
2 isset 2805 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbir 200 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:   E.wex 1531    = wceq 1632    e. wcel 1696   _Vcvv 2801
This theorem is referenced by:  zfrep4  4155  0ex  4166  inex1  4171  pwex  4209  zfpair2  4231  uniex  4532
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-v 2803
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