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Theorem nfsymdif 3233
 Description: Hypothesis builder for symmetric difference. (Contributed by SF, 2-Jan-2018.)
Hypotheses
Ref Expression
nfbool.1 xA
nfbool.2 xB
Assertion
Ref Expression
nfsymdif x(AB)

Proof of Theorem nfsymdif
StepHypRef Expression
1 df-symdif 3216 . 2 (AB) = ((A B) ∪ (B A))
2 nfbool.1 . . . 4 xA
3 nfbool.2 . . . 4 xB
42, 3nfdif 3232 . . 3 x(A B)
53, 2nfdif 3232 . . 3 x(B A)
64, 5nfun 3231 . 2 x((A B) ∪ (B A))
71, 6nfcxfr 2486 1 x(AB)
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2476   ∖ cdif 3206   ∪ cun 3207   ⊕ csymdif 3209 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216 This theorem is referenced by: (None)
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