Theorem isseti 2866

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

Hypothesis

Ref	Expression
isseti.1	⊢ A ∈ V

Assertion

Ref	Expression
isseti	⊢ ∃x x = A

Distinct variable group:   x,A

Proof of Theorem isseti

Step	Hyp	Ref	Expression
1		isseti.1	. 2 ⊢ A ∈ V
2		isset 2864	. 2 ⊢ (A ∈ V ↔ ∃x x = A)
3	1, 2	mpbi 199	1 ⊢ ∃x x = A

Syntax hints:  ∃wex 1541   = wceq 1642   ∈ wcel 1710  Vcvv 2860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2862

This theorem is referenced by:  rexcom4b  2881  ceqsex  2894  vtoclf  2909  vtocl2  2911  vtocl3  2912  vtoclef  2928  eqvinc  2967  euind  3024  opabn0  4717  dmsi  5520  rnoprab  5577  ov3  5600  dmtxp  5803  dmpprod  5841