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Theorem symdifeq2 25666
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 25665 . 2  |-  ( A  =  B  ->  ( A(++) C )  =  ( B(++) C ) )
2 symdifcom 25664 . 2  |-  ( C(++) A )  =  ( A(++) C )
3 symdifcom 25664 . 2  |-  ( C(++) B )  =  ( B(++) C )
41, 2, 33eqtr4g 2493 1  |-  ( A  =  B  ->  ( C(++) A )  =  ( C(++) B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652  (++)csymdif 25662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-symdif 25663
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