Theorem issetri 2923

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 2920	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 201	1 |- A e. _V

Syntax hints:   E.wex 1547   = wceq 1649   e. wcel 1721   _Vcvv 2916

This theorem is referenced by:  zfrep4  4288  0ex  4299  inex1  4304  pwex  4342  zfpair2  4364  uniex  4664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-ext 2385

This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-v 2918