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Theorem issetri 2907
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 2904 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbir 201 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:   E.wex 1547    = wceq 1649    e. wcel 1717   _Vcvv 2900
This theorem is referenced by:  zfrep4  4270  0ex  4281  inex1  4286  pwex  4324  zfpair2  4346  uniex  4646
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-v 2902
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