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Theorem issetri 3314
Description: A way to say "𝐴 is a set" (inference rule). (Contributed by NM, 21-Jun-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 3311 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 221 1 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1596  wex 1817  wcel 2103  Vcvv 3304
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-12 2160  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1599  df-ex 1818  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-v 3306
This theorem is referenced by:  zfrep4  4887  0ex  4898  inex1  4907  pwex  4953  zfpair2  5012  uniex  7070  bj-snsetex  33178
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