Theorem isseti 2607

Description: A way to say " A is a set" (inference rule). (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 2605	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbi 143	1 |- E. x x = A

Syntax hints:   = wceq 1284   E.wex 1421   e. wcel 1433   _Vcvv 2601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by:  rexcom4b  2624  ceqsex  2637  vtoclf  2652  vtocl2  2654  vtocl3  2655  vtoclef  2671  eqvinc  2718  euind  2779  opabm  4035  eusv2nf  4206  dtruex  4302  limom  4354  isarep2  5006  dfoprab2  5572  rnoprab  5607  dmaddpq  6569  dmmulpq  6570  bj-inf2vnlem1  10765