Theorem issetri 2564

Description: A way to say " A is a set" (inference rule). (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 2561	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 134	1 |- A e. _V

Syntax hints:   = wceq 1243   E.wex 1381   e. wcel 1393   _Vcvv 2557

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559

This theorem is referenced by:  0ex  3884  inex1  3891  pwex  3932  zfpair2  3945  uniex  4174  bdinex1  10019  bj-zfpair2  10030  bj-uniex  10037  bj-omex2  10102