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Theorem issetri 2558
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 2555 . 2 (A V ↔ x x = A)
31, 2mpbir 134 1 A V
Colors of variables: wff set class
Syntax hints:   = wceq 1242  wex 1378   wcel 1390  Vcvv 2551
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  0ex  3875  inex1  3882  pwex  3923  zfpair2  3936  uniex  4140  bdinex1  9284  bj-zfpair2  9295  bj-uniex  9302  bj-omex2  9361
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