Theorem isseti 2689

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 2687	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbi 144	1 |- E. x x = A

Syntax hints:   = wceq 1331   E.wex 1468   e. wcel 1480   _Vcvv 2681

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683

This theorem is referenced by:  rexcom4b  2706  ceqsex  2719  vtoclf  2734  vtocl2  2736  vtocl3  2737  vtoclef  2754  eqvinc  2803  euind  2866  opabm  4197  eusv2nf  4372  dtruex  4469  limom  4522  isarep2  5205  dfoprab2  5811  rnoprab  5847  dmaddpq  7180  dmmulpq  7181  bj-inf2vnlem1  13157