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Theorem dfsymdif2 4180
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 4179 . 2 (𝑥 ∈ (𝐴𝐵) ↔ (𝑥𝐴𝑥𝐵))
21abbi2i 2932 1 (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Colors of variables: wff setvar class
Syntax hints:  wxo 1502   = wceq 1538  wcel 2112  {cab 2779  csymdif 4171
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-xor 1503  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-dif 3887  df-un 3889  df-symdif 4172
This theorem is referenced by: (None)
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