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Theorem nfsymdif 4105
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 4101 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
2 nfsymdif.1 . . . 4 𝑥𝐴
3 nfsymdif.2 . . . 4 𝑥𝐵
42, 3nfdif 3988 . . 3 𝑥(𝐴𝐵)
53, 2nfdif 3988 . . 3 𝑥(𝐵𝐴)
64, 5nfun 4026 . 2 𝑥((𝐴𝐵) ∪ (𝐵𝐴))
71, 6nfcxfr 2924 1 𝑥(𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2910  cdif 3822  cun 3823  csymdif 4100
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1964  ax-8 2050  ax-9 2057  ax-10 2077  ax-11 2091  ax-12 2104  ax-13 2299  ax-ext 2745
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2014  df-clab 2754  df-cleq 2765  df-clel 2840  df-nfc 2912  df-rab 3091  df-dif 3828  df-un 3830  df-symdif 4101
This theorem is referenced by: (None)
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