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Theorem eqvisset 2565
 Description: A class equal to a variable is a set. Note the absence of dv condition, contrary to isset 2561 and issetri 2564. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset (𝑥 = 𝐴𝐴 ∈ V)

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 2560 . 2 𝑥 ∈ V
2 eleq1 2100 . 2 (𝑥 = 𝐴 → (𝑥 ∈ V ↔ 𝐴 ∈ V))
31, 2mpbii 136 1 (𝑥 = 𝐴𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243   ∈ wcel 1393  Vcvv 2557 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by:  xpsnen  6295
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