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Theorem nfsymdif 3840
 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 𝑥𝐴
nfsymdif.2 𝑥𝐵
Assertion
Ref Expression
nfsymdif 𝑥(𝐴𝐵)

Proof of Theorem nfsymdif
StepHypRef Expression
1 df-symdif 3836 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
2 nfsymdif.1 . . . 4 𝑥𝐴
3 nfsymdif.2 . . . 4 𝑥𝐵
42, 3nfdif 3723 . . 3 𝑥(𝐴𝐵)
53, 2nfdif 3723 . . 3 𝑥(𝐵𝐴)
64, 5nfun 3761 . 2 𝑥((𝐴𝐵) ∪ (𝐵𝐴))
71, 6nfcxfr 2760 1 𝑥(𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2749   ∖ cdif 3564   ∪ cun 3565   △ csymdif 3835 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rab 2918  df-dif 3570  df-un 3572  df-symdif 3836 This theorem is referenced by: (None)
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