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Theorem symdifeq2 24436
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 24435 . 2  |-  ( A  =  B  ->  ( A(++) C )  =  ( B(++) C ) )
2 symdifcom 24434 . 2  |-  ( C(++) A )  =  ( A(++) C )
3 symdifcom 24434 . 2  |-  ( C(++) B )  =  ( B(++) C )
41, 2, 33eqtr4g 2353 1  |-  ( A  =  B  ->  ( C(++) A )  =  ( C(++) B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632  (++)csymdif 24432
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-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-symdif 24433
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