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Theorem symdifcom 4102
 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 4014 . 2 ((𝐴𝐵) ∪ (𝐵𝐴)) = ((𝐵𝐴) ∪ (𝐴𝐵))
2 df-symdif 4101 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
3 df-symdif 4101 . 2 (𝐵𝐴) = ((𝐵𝐴) ∪ (𝐴𝐵))
41, 2, 33eqtr4i 2806 1 (𝐴𝐵) = (𝐵𝐴)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1507   ∖ cdif 3822   ∪ cun 3823   △ csymdif 4100 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1964  ax-8 2050  ax-9 2057  ax-10 2077  ax-11 2091  ax-12 2104  ax-ext 2745 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2014  df-clab 2754  df-cleq 2765  df-clel 2840  df-nfc 2912  df-v 3411  df-un 3830  df-symdif 4101 This theorem is referenced by:  symdifeq2  4104
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