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Theorem eqvisset 2643
 Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2639 and issetri 2642. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset (𝑥 = 𝐴𝐴 ∈ V)

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 2636 . 2 𝑥 ∈ V
2 eleq1 2157 . 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 1296   ∈ wcel 1445  Vcvv 2633 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 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-v 2635 This theorem is referenced by:  elxp5  4953  xpsnen  6617
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