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Theorem eqvisset 2747
Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2743 and issetri 2746. (Contributed by BJ, 27-Apr-2019.)
Assertion
Ref Expression
eqvisset (𝑥 = 𝐴𝐴 ∈ V)

Proof of Theorem eqvisset
StepHypRef Expression
1 vex 2740 . 2 𝑥 ∈ V
2 eleq1 2240 . 2 (𝑥 = 𝐴 → (𝑥 ∈ V ↔ 𝐴 ∈ V))
31, 2mpbii 148 1 (𝑥 = 𝐴𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wcel 2148  Vcvv 2737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2739
This theorem is referenced by:  elxp5  5112  xpsnen  6814  fival  6962
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