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Theorem issetri 2746
Description: A way to say " A is a set" (inference form). (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 2743 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbir 146 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1353   E.wex 1492    e. wcel 2148   _Vcvv 2737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2739
This theorem is referenced by:  0ex  4128  inex1  4135  vpwex  4177  zfpair2  4208  uniex  4435  bdinex1  14455  bj-zfpair2  14466  bj-uniex  14473  bj-omex2  14533
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