Theorem isseti 2665

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 2663	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbi 144	1 |- E. x x = A

Syntax hints:   = wceq 1314   E.wex 1451   e. wcel 1463   _Vcvv 2657

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-v 2659

This theorem is referenced by:  rexcom4b  2682  ceqsex  2695  vtoclf  2710  vtocl2  2712  vtocl3  2713  vtoclef  2730  eqvinc  2778  euind  2840  opabm  4162  eusv2nf  4337  dtruex  4434  limom  4487  isarep2  5168  dfoprab2  5772  rnoprab  5808  dmaddpq  7135  dmmulpq  7136  bj-inf2vnlem1  12860