Theorem isseti 2808

Description: A way to say " A is a set" (inference form). (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
isseti.1	|- A e. _V

Assertion

Ref	Expression
isseti	|- E. x x = A

Distinct variable group:   x, A

Proof of Theorem isseti

Step	Hyp	Ref	Expression
1		isseti.1	. 2 |- A e. _V
2		isset 2806	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbi 145	1 |- E. x x = A

Syntax hints:   = wceq 1395   E.wex 1538   e. wcel 2200   _Vcvv 2799

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-v 2801

This theorem is referenced by:  rexcom4b  2825  ceqsex  2838  ceqsexv2d  2840  vtoclf  2854  vtocl2  2856  vtocl3  2857  vtoclef  2876  eqvinc  2926  euind  2990  opabm  4369  eusv2nf  4547  dtruex  4651  limom  4706  isarep2  5408  dfoprab2  6051  rnoprab  6087  dmaddpq  7566  dmmulpq  7567  bj-inf2vnlem1  16333