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Theorem nfsymdif 4245
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 4241 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
2 nfsymdif.1 . . . 4 𝑥𝐴
3 nfsymdif.2 . . . 4 𝑥𝐵
42, 3nfdif 4121 . . 3 𝑥(𝐴𝐵)
53, 2nfdif 4121 . . 3 𝑥(𝐵𝐴)
64, 5nfun 4162 . 2 𝑥((𝐴𝐵) ∪ (𝐵𝐴))
71, 6nfcxfr 2889 1 𝑥(𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2875  cdif 3941  cun 3942  csymdif 4240
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-v 3463  df-dif 3947  df-un 3949  df-symdif 4241
This theorem is referenced by: (None)
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