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Theorem dfsymdif2 4245
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 4244 . 2 (𝑥 ∈ (𝐴𝐵) ↔ (𝑥𝐴𝑥𝐵))
21eqabi 2863 1 (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Colors of variables: wff setvar class
Syntax hints:  wxo 1504   = wceq 1533  wcel 2098  {cab 2703  csymdif 4236
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-xor 1505  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-dif 3946  df-un 3948  df-symdif 4237
This theorem is referenced by: (None)
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