Theorem issetri 3210

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 3207	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 221	1 |- A e. _V

Syntax hints:   = wceq 1483   E.wex 1704   e. wcel 1990   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202

This theorem is referenced by:  zfrep4  4779  0ex  4790  inex1  4799  pwex  4848  zfpair2  4907  uniex  6953  bj-snsetex  32951