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Theorem dfsymdif2 4249
Description: Alternate definition of the symmetric difference. (Contributed by BJ, 30-Apr-2020.)
Assertion
Ref Expression
dfsymdif2 (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Proof of Theorem dfsymdif2
StepHypRef Expression
1 elsymdifxor 4248 . 2 (𝑥 ∈ (𝐴𝐵) ↔ (𝑥𝐴𝑥𝐵))
21eqabi 2862 1 (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Colors of variables: wff setvar class
Syntax hints:  wxo 1505   = wceq 1534  wcel 2099  {cab 2703  csymdif 4240
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-xor 1506  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-dif 3949  df-un 3951  df-symdif 4241
This theorem is referenced by: (None)
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