Theorem issetri 2812

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 2809	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 146	1 |- A e. _V

Syntax hints:   = wceq 1397   E.wex 1540   e. wcel 2202   _Vcvv 2802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804

This theorem is referenced by:  0ex  4216  inex1  4223  vpwex  4269  zfpair2  4300  uniex  4534  bdinex1  16494  bj-zfpair2  16505  bj-uniex  16512  bj-omex2  16572