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Theorem nfsymdif 3729
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 3725 . 2  |-  ( A  /_\  B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
2 nfsymdif.1 . . . 4  |-  F/_ x A
3 nfsymdif.2 . . . 4  |-  F/_ x B
42, 3nfdif 3621 . . 3  |-  F/_ x
( A  \  B
)
53, 2nfdif 3621 . . 3  |-  F/_ x
( B  \  A
)
64, 5nfun 3656 . 2  |-  F/_ x
( ( A  \  B )  u.  ( B  \  A ) )
71, 6nfcxfr 2617 1  |-  F/_ x
( A  /_\  B )
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2605    \ cdif 3468    u. cun 3469    /_\ csymdif 3724
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-dif 3474  df-un 3476  df-symdif 3725
This theorem is referenced by: (None)
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