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Theorem symdifcom 4037
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 3950 . 2 ((𝐴𝐵) ∪ (𝐵𝐴)) = ((𝐵𝐴) ∪ (𝐴𝐵))
2 df-symdif 4036 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
3 df-symdif 4036 . 2 (𝐵𝐴) = ((𝐵𝐴) ∪ (𝐴𝐵))
41, 2, 33eqtr4i 2834 1 (𝐴𝐵) = (𝐵𝐴)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1637  cdif 3760  cun 3761  csymdif 4035
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2067  ax-7 2103  ax-9 2164  ax-10 2184  ax-11 2200  ax-12 2213  ax-13 2419  ax-ext 2781
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2060  df-clab 2789  df-cleq 2795  df-clel 2798  df-nfc 2933  df-v 3389  df-un 3768  df-symdif 4036
This theorem is referenced by:  symdifeq2  4039
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