Theorem isseti 2729

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 2727	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	mpbi 144	1 |- E. x x = A

Syntax hints:   = wceq 1342   E.wex 1479   e. wcel 2135   _Vcvv 2721

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 1434  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-v 2723

This theorem is referenced by:  rexcom4b  2746  ceqsex  2759  vtoclf  2774  vtocl2  2776  vtocl3  2777  vtoclef  2794  eqvinc  2844  euind  2908  opabm  4252  eusv2nf  4428  dtruex  4530  limom  4585  isarep2  5269  dfoprab2  5880  rnoprab  5916  dmaddpq  7311  dmmulpq  7312  bj-inf2vnlem1  13687