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Theorem symdifid 4411
 Description: Symmetric difference with self yields the empty class. (Contributed by Scott Fenton, 25-Apr-2012.)
Assertion
Ref Expression
symdifid

Proof of Theorem symdifid
StepHypRef Expression
1 df-symdif 3725 . 2
2 difid 3899 . . 3
32, 2uneq12i 3652 . 2
4 un0 3819 . 2
51, 3, 43eqtri 2490 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1395   cdif 3468   cun 3469   csymdif 3724  c0 3793 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-symdif 3725  df-nul 3794 This theorem is referenced by: (None)
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