Theorem issetri 2608

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

Step	Hyp	Ref	Expression
1		issetri.1	. 2 |- E. x x = A
2		isset 2605	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 144	1 |- A e. _V

Syntax hints:   = wceq 1284   E.wex 1421   e. wcel 1433   _Vcvv 2601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by:  0ex  3905  inex1  3912  pwex  3953  zfpair2  3965  uniex  4192  bdinex1  10690  bj-zfpair2  10701  bj-uniex  10708  bj-omex2  10772