Theorem issetri 2984

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

Step	Hyp	Ref	Expression
1		issetri.1	. 2 |- E. x x = A
2		isset 2981	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 209	1 |- A e. _V

Syntax hints:   = wceq 1369   E.wex 1586   e. wcel 1756   _Vcvv 2977

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792  ax-ext 2423

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-v 2979

This theorem is referenced by:  zfrep4  4416  0ex  4427  inex1  4438  pwex  4480  zfpair2  4537  uniex  6381  bj-snsetex  32461