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Theorem symdifeq2 3675
Description: Equality theorem for symmetric difference. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdifeq2  |-  ( A  =  B  ->  ( C  /_\  A )  =  ( C  /_\  B ) )

Proof of Theorem symdifeq2
StepHypRef Expression
1 symdifeq1 3674 . 2  |-  ( A  =  B  ->  ( A  /_\  C )  =  ( B  /_\  C ) )
2 symdifcom 3673 . 2  |-  ( C  /_\  A )  =  ( A  /_\  C )
3 symdifcom 3673 . 2  |-  ( C  /_\  B )  =  ( B  /_\  C )
41, 2, 33eqtr4g 2470 1  |-  ( A  =  B  ->  ( C  /_\  A )  =  ( C  /_\  B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1407    /_\ csymdif 3671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382
This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ral 2761  df-rab 2765  df-v 3063  df-dif 3419  df-un 3421  df-symdif 3672
This theorem is referenced by: (None)
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