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Theorem nfsymdif 3810
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 3806 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
2 nfsymdif.1 . . . 4 𝑥𝐴
3 nfsymdif.2 . . . 4 𝑥𝐵
42, 3nfdif 3693 . . 3 𝑥(𝐴𝐵)
53, 2nfdif 3693 . . 3 𝑥(𝐵𝐴)
64, 5nfun 3731 . 2 𝑥((𝐴𝐵) ∪ (𝐵𝐴))
71, 6nfcxfr 2749 1 𝑥(𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2738  cdif 3537  cun 3538  csymdif 3805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-dif 3543  df-un 3545  df-symdif 3806
This theorem is referenced by: (None)
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