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Theorem issetri 2542
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 2539 . 2 (A V ↔ x x = A)
31, 2mpbir 134 1 A V
Colors of variables: wff set class
Syntax hints:   = wceq 1228  wex 1362   wcel 1374  Vcvv 2535
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 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-v 2537
This theorem is referenced by:  0ex  3858  inex1  3865  pwex  3906  zfpair2  3919  uniex  4124  bdinex1  7122  bj-zfpair2  7133  bj-uniex  7140  bj-omex2  7195
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