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Theorem symdifcom 3700
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 3616 . 2  |-  ( ( A  \  B )  u.  ( B  \  A ) )  =  ( ( B  \  A )  u.  ( A  \  B ) )
2 df-symdif 3699 . 2  |-  ( A  /_\  B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
3 df-symdif 3699 . 2  |-  ( B  /_\  A )  =  ( ( B  \  A
)  u.  ( A 
\  B ) )
41, 2, 33eqtr4i 2468 1  |-  ( A  /_\  B )  =  ( B  /_\  A )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    \ cdif 3439    u. cun 3440    /_\ csymdif 3698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-un 3447  df-symdif 3699
This theorem is referenced by:  symdifeq2  3702
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