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Theorem nfsymdif 24366
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 24362 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
2 nfsymdif.1 . . . 4  |-  F/_ x A
3 nfsymdif.2 . . . 4  |-  F/_ x B
42, 3nfdif 3297 . . 3  |-  F/_ x
( A  \  B
)
53, 2nfdif 3297 . . 3  |-  F/_ x
( B  \  A
)
64, 5nfun 3331 . 2  |-  F/_ x
( ( A  \  B )  u.  ( B  \  A ) )
71, 6nfcxfr 2416 1  |-  F/_ x
( A(++) B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406    \ cdif 3149    u. cun 3150  (++)csymdif 24361
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-dif 3155  df-un 3157  df-symdif 24362
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