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Theorem eqvisset 3364
Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 3360 and issetri 3363. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset (𝑥 = 𝐴𝐴 ∈ V)

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 3353 . 2 𝑥 ∈ V
2 eleq1 2832 . 2 (𝑥 = 𝐴 → (𝑥 ∈ V ↔ 𝐴 ∈ V))
31, 2mpbii 224 1 (𝑥 = 𝐴𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1652  wcel 2155  Vcvv 3350
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-tru 1656  df-ex 1875  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-v 3352
This theorem is referenced by:  ceqex  3486  moeq3  3542  mo2icl  3544  eusvnfb  5028  oprabv  6901  elxp5  7309  xpsnen  8251  fival  8525  dffi2  8536  tz9.12lem1  8865  m1detdiag  20680  dvfsumlem1  24080  dchrisumlema  25468  dchrisumlem2  25470  fnimage  32412  bj-csbsnlem  33255  disjf1o  39957  mptssid  40024  fourierdlem49  40941
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