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Theorem issetri 2984
Description: A way to say " A is a set" (inference rule). (Contributed by NM, 21-Jun-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 2981 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbir 209 1  |-  A  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369   E.wex 1586    e. wcel 1756   _Vcvv 2977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-v 2979
This theorem is referenced by:  zfrep4  4416  0ex  4427  inex1  4438  pwex  4480  zfpair2  4537  uniex  6381  bj-snsetex  32461
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