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Theorem isseti 2807
Description: A way to say " A is a set" (inference rule). (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
isseti.1  |-  A  e. 
_V
Assertion
Ref Expression
isseti  |-  E. x  x  =  A
Distinct variable group:    x, A

Proof of Theorem isseti
StepHypRef Expression
1 isseti.1 . 2  |-  A  e. 
_V
2 isset 2805 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbi 199 1  |-  E. x  x  =  A
Colors of variables: wff set class
Syntax hints:   E.wex 1531    = wceq 1632    e. wcel 1696   _Vcvv 2801
This theorem is referenced by:  rexcom4b  2822  ceqsex  2835  vtoclf  2850  vtocl2  2852  vtocl3  2853  vtoclef  2869  eqvinc  2908  euind  2965  zfpair  4228  axpr  4229  opabn0  4311  eusv2nf  4548  isarep2  5348  dfoprab2  5911  rnoprab  5946  ov3  6000  omeu  6599  cflem  7888  genpass  8649  supmul1  9735  supmullem2  9737  supmul  9738  uzindOLD  10122  ruclem13  12536  supaddc  24995  supadd  24996  dmoprabss6  25138  cmppar2  26075  bnj986  29302
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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