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Theorem nfsymdif 25383
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 25379 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
2 nfsymdif.1 . . . 4  |-  F/_ x A
3 nfsymdif.2 . . . 4  |-  F/_ x B
42, 3nfdif 3404 . . 3  |-  F/_ x
( A  \  B
)
53, 2nfdif 3404 . . 3  |-  F/_ x
( B  \  A
)
64, 5nfun 3439 . 2  |-  F/_ x
( ( A  \  B )  u.  ( B  \  A ) )
71, 6nfcxfr 2513 1  |-  F/_ x
( A(++) B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2503    \ cdif 3253    u. cun 3254  (++)csymdif 25378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-rab 2651  df-dif 3259  df-un 3261  df-symdif 25379
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