Theorem issetri 2650

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

Step	Hyp	Ref	Expression
1		issetri.1	. 2 |- E. x x = A
2		isset 2647	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 145	1 |- A e. _V

Syntax hints:   = wceq 1299   E.wex 1436   e. wcel 1448   _Vcvv 2641

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-ext 2082

This theorem depends on definitions:  df-bi 116  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-v 2643

This theorem is referenced by:  0ex  3995  inex1  4002  vpwex  4043  zfpair2  4070  uniex  4297  bdinex1  12678  bj-zfpair2  12689  bj-uniex  12696  bj-omex2  12760