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Theorem issetri 3116
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 3113 . 2  |-  ( A  e.  _V  <->  E. x  x  =  A )
31, 2mpbir 209 1  |-  A  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1395   E.wex 1613    e. wcel 1819   _Vcvv 3109
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-12 1855  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
This theorem is referenced by:  zfrep4  4576  0ex  4587  inex1  4597  pwex  4639  zfpair2  4696  uniex  6595  bj-snsetex  34622
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