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Theorem eqvisset 2700
 Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2696 and issetri 2699. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset (𝑥 = 𝐴𝐴 ∈ V)

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 2693 . 2 𝑥 ∈ V
2 eleq1 2203 . 2 (𝑥 = 𝐴 → (𝑥 ∈ V ↔ 𝐴 ∈ V))
31, 2mpbii 147 1 (𝑥 = 𝐴𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1332   ∈ wcel 1481  Vcvv 2690 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 2692 This theorem is referenced by:  elxp5  5038  xpsnen  6726  fival  6874
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