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Theorem nfsymdif 25659
Description: Hypothesis builder for symmetric difference. (Contributed by Scott Fenton, 19-Feb-2013.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
nfsymdif.1  |-  F/_ x A
nfsymdif.2  |-  F/_ x B
Assertion
Ref Expression
nfsymdif  |-  F/_ x
( A(++) B )

Proof of Theorem nfsymdif
StepHypRef Expression
1 df-symdif 25655 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
2 nfsymdif.1 . . . 4  |-  F/_ x A
3 nfsymdif.2 . . . 4  |-  F/_ x B
42, 3nfdif 3460 . . 3  |-  F/_ x
( A  \  B
)
53, 2nfdif 3460 . . 3  |-  F/_ x
( B  \  A
)
64, 5nfun 3495 . 2  |-  F/_ x
( ( A  \  B )  u.  ( B  \  A ) )
71, 6nfcxfr 2568 1  |-  F/_ x
( A(++) B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2558    \ cdif 3309    u. cun 3310  (++)csymdif 25654
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 2416
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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-dif 3315  df-un 3317  df-symdif 25655
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