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Theorem nfsymdif 4208
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 4204 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
2 nfsymdif.1 . . . 4 𝑥𝐴
3 nfsymdif.2 . . . 4 𝑥𝐵
42, 3nfdif 4088 . . 3 𝑥(𝐴𝐵)
53, 2nfdif 4088 . . 3 𝑥(𝐵𝐴)
64, 5nfun 4127 . 2 𝑥((𝐴𝐵) ∪ (𝐵𝐴))
71, 6nfcxfr 2980 1 𝑥(𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2962  cdif 3916  cun 3917  csymdif 4203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3142  df-dif 3922  df-un 3924  df-symdif 4204
This theorem is referenced by: (None)
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