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Theorem symdifcom 24434
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 3332 . 2  |-  ( ( A  \  B )  u.  ( B  \  A ) )  =  ( ( B  \  A )  u.  ( A  \  B ) )
2 df-symdif 24433 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
3 df-symdif 24433 . 2  |-  ( B(++) A )  =  ( ( B  \  A
)  u.  ( A 
\  B ) )
41, 2, 33eqtr4i 2326 1  |-  ( A(++) B )  =  ( B(++) A )
Colors of variables: wff set class
Syntax hints:    = wceq 1632    \ cdif 3162    u. cun 3163  (++)csymdif 24432
This theorem is referenced by:  symdifeq2  24436
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-symdif 24433
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