Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfsymdif Unicode version

Theorem nfsymdif 24437
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 24433 . 2  |-  ( A(++) B )  =  ( ( A  \  B
)  u.  ( B 
\  A ) )
2 nfsymdif.1 . . . 4  |-  F/_ x A
3 nfsymdif.2 . . . 4  |-  F/_ x B
42, 3nfdif 3310 . . 3  |-  F/_ x
( A  \  B
)
53, 2nfdif 3310 . . 3  |-  F/_ x
( B  \  A
)
64, 5nfun 3344 . 2  |-  F/_ x
( ( A  \  B )  u.  ( B  \  A ) )
71, 6nfcxfr 2429 1  |-  F/_ x
( A(++) B )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419    \ cdif 3162    u. cun 3163  (++)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-rab 2565  df-dif 3168  df-un 3170  df-symdif 24433
  Copyright terms: Public domain W3C validator