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Theorem symdif0 4409
Description: Symmetric difference with the empty class. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdif0  |-  ( A  /_\  (/) )  =  A

Proof of Theorem symdif0
StepHypRef Expression
1 df-symdif 3725 . 2  |-  ( A  /_\  (/) )  =  ( ( A  \  (/) )  u.  ( (/)  \  A ) )
2 dif0 3901 . . 3  |-  ( A 
\  (/) )  =  A
3 0dif 3902 . . 3  |-  ( (/)  \  A )  =  (/)
42, 3uneq12i 3652 . 2  |-  ( ( A  \  (/) )  u.  ( (/)  \  A ) )  =  ( A  u.  (/) )
5 un0 3819 . 2  |-  ( A  u.  (/) )  =  A
61, 4, 53eqtri 2490 1  |-  ( A  /_\  (/) )  =  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1395    \ cdif 3468    u. 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-ral 2812  df-rab 2816  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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