Theorem issetri 3116

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 3113	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 209	1 |- A e. _V

Syntax hints:   = wceq 1395   E.wex 1613   e. wcel 1819   _Vcvv 3109

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-12 1855  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111

This theorem is referenced by:  zfrep4  4576  0ex  4587  inex1  4597  pwex  4639  zfpair2  4696  uniex  6595  bj-snsetex  34622