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Theorem issetri 3183
 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 3180 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 220 1 𝐴 ∈ V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ∃wex 1695   ∈ wcel 1977  Vcvv 3173 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-tru 1478  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-v 3175 This theorem is referenced by:  zfrep4  4707  0ex  4718  inex1  4727  pwex  4774  zfpair2  4834  uniex  6851  bj-snsetex  32144
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