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Theorem issetri 2650
Description: A way to say "𝐴 is a set" (inference form). (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 2647 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbir 145 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:   = wceq 1299  wex 1436  wcel 1448  Vcvv 2641
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-v 2643
This theorem is referenced by:  0ex  3995  inex1  4002  vpwex  4043  zfpair2  4070  uniex  4297  bdinex1  12678  bj-zfpair2  12689  bj-uniex  12696  bj-omex2  12760
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