MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  issetri Structured version   Unicode version

Theorem issetri 2955
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 2952 . 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 1550    = wceq 1652    e. wcel 1725   _Vcvv 2948
This theorem is referenced by:  zfrep4  4320  0ex  4331  inex1  4336  pwex  4374  zfpair2  4396  uniex  4697
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
  Copyright terms: Public domain W3C validator