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Theorem symdifcom 4173
 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 4083 . 2 ((𝐴𝐵) ∪ (𝐵𝐴)) = ((𝐵𝐴) ∪ (𝐴𝐵))
2 df-symdif 4172 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
3 df-symdif 4172 . 2 (𝐵𝐴) = ((𝐵𝐴) ∪ (𝐴𝐵))
41, 2, 33eqtr4i 2834 1 (𝐴𝐵) = (𝐵𝐴)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∖ cdif 3881   ∪ cun 3882   △ 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-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-symdif 4172 This theorem is referenced by:  symdifeq2  4175
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