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Theorem symdifcom 3807
 Description: Symmetric difference commutes. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdifcom (𝐴𝐵) = (𝐵𝐴)

Proof of Theorem symdifcom
StepHypRef Expression
1 uncom 3719 . 2 ((𝐴𝐵) ∪ (𝐵𝐴)) = ((𝐵𝐴) ∪ (𝐴𝐵))
2 df-symdif 3806 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
3 df-symdif 3806 . 2 (𝐵𝐴) = ((𝐵𝐴) ∪ (𝐴𝐵))
41, 2, 33eqtr4i 2642 1 (𝐴𝐵) = (𝐵𝐴)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∖ cdif 3537   ∪ cun 3538   △ csymdif 3805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-symdif 3806 This theorem is referenced by:  symdifeq2  3809
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