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Theorem symdifcom 24363
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 3319 . 2  |-  ( ( A  \  B )  u.  ( B  \  A ) )  =  ( ( B  \  A )  u.  ( A  \  B ) )
2 df-symdif 24362 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
3 df-symdif 24362 . 2  |-  ( B(++) A )  =  ( ( B  \  A
)  u.  ( A 
\  B ) )
41, 2, 33eqtr4i 2313 1  |-  ( A(++) B )  =  ( B(++) A )
Colors of variables: wff set class
Syntax hints:    = wceq 1623    \ cdif 3149    u. cun 3150  (++)csymdif 24361
This theorem is referenced by:  symdifeq2  24365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-symdif 24362
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