Theorem issetri 3064

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 3061	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 214	1 |- A e. _V

Syntax hints:   = wceq 1455   E.wex 1674   e. wcel 1898   _Vcvv 3057

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944  ax-ext 2442

This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-v 3059

This theorem is referenced by:  zfrep4  4537  0ex  4549  inex1  4558  pwex  4600  zfpair2  4654  uniex  6614  bj-snsetex  31602