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Theorem isseti 2865
 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
StepHypRef Expression
1 isseti.1 . 2 A V
2 isset 2863 . 2 (A V ↔ x x = A)
31, 2mpbi 199 1 x x = A
 Colors of variables: wff setvar class Syntax hints:  ∃wex 1541   = wceq 1642   ∈ wcel 1710  Vcvv 2859 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 2861 This theorem is referenced by:  rexcom4b  2880  ceqsex  2893  vtoclf  2908  vtocl2  2910  vtocl3  2911  vtoclef  2927  eqvinc  2966  euind  3023  opabn0  4716  dmsi  5519  rnoprab  5576  ov3  5599  dmtxp  5802  dmpprod  5840
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