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Theorem isseti 2697
 Description: A way to say "𝐴 is a set" (inference form). (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
isseti.1 𝐴 ∈ V
Assertion
Ref Expression
isseti 𝑥 𝑥 = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem isseti
StepHypRef Expression
1 isseti.1 . 2 𝐴 ∈ V
2 isset 2695 . 2 (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
31, 2mpbi 144 1 𝑥 𝑥 = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1332  ∃wex 1469   ∈ wcel 1481  Vcvv 2689 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-v 2691 This theorem is referenced by:  rexcom4b  2714  ceqsex  2727  vtoclf  2742  vtocl2  2744  vtocl3  2745  vtoclef  2762  eqvinc  2811  euind  2874  opabm  4209  eusv2nf  4384  dtruex  4481  limom  4534  isarep2  5217  dfoprab2  5825  rnoprab  5861  dmaddpq  7210  dmmulpq  7211  bj-inf2vnlem1  13337
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