Theorem issetri 2769

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 2766	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbir 146	1 |- A e. _V

Syntax hints:   = wceq 1364   E.wex 1503   e. wcel 2164   _Vcvv 2760

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762

This theorem is referenced by:  0ex  4156  inex1  4163  vpwex  4208  zfpair2  4239  uniex  4468  bdinex1  15391  bj-zfpair2  15402  bj-uniex  15409  bj-omex2  15469