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Theorem issetri 2541
 Description: A way to say "A is a set" (inference rule). (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
issetri.1 x x = A
Assertion
Ref Expression
issetri A V
Distinct variable group:   x,A

Proof of Theorem issetri
StepHypRef Expression
1 issetri.1 . 2 x x = A
2 isset 2538 . 2 (A V ↔ x x = A)
31, 2mpbir 134 1 A V
 Colors of variables: wff set class Syntax hints:  ∃wex 1362   = wceq 1374   ∈ wcel 1376  Vcvv 2534 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1378  ax-4 1383  ax-17 1402  ax-i9 1406  ax-ial 1411  ax-ext 2005 This theorem depends on definitions:  df-bi 110  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-v 2536 This theorem is referenced by:  0ex  3837  inex1  3844  pwex  3885  zfpair2  3898  uniex  4100
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