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Theorem symdifcom 29074
Description: Symmetric difference commutes. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdifcom  |-  ( A(++) B )  =  ( B(++) A )

Proof of Theorem symdifcom
StepHypRef Expression
1 uncom 3648 . 2  |-  ( ( A  \  B )  u.  ( B  \  A ) )  =  ( ( B  \  A )  u.  ( A  \  B ) )
2 df-symdif 29073 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
3 df-symdif 29073 . 2  |-  ( B(++) A )  =  ( ( B  \  A
)  u.  ( A 
\  B ) )
41, 2, 33eqtr4i 2506 1  |-  ( A(++) B )  =  ( B(++) A )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    \ cdif 3473    u. cun 3474  (++)csymdif 29072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481  df-symdif 29073
This theorem is referenced by:  symdifeq2  29076
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