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Theorem symdifid 4902
 Description: The symmetric difference of a class with itself is the empty class. (Contributed by Scott Fenton, 25-Apr-2012.)
Assertion
Ref Expression
symdifid (𝐴𝐴) = ∅

Proof of Theorem symdifid
StepHypRef Expression
1 df-symdif 4134 . 2 (𝐴𝐴) = ((𝐴𝐴) ∪ (𝐴𝐴))
2 difid 4244 . . 3 (𝐴𝐴) = ∅
32, 2uneq12i 4053 . 2 ((𝐴𝐴) ∪ (𝐴𝐴)) = (∅ ∪ ∅)
4 un0 4258 . 2 (∅ ∪ ∅) = ∅
51, 3, 43eqtri 2821 1 (𝐴𝐴) = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1520   ∖ cdif 3851   ∪ cun 3852   △ csymdif 4133  ∅c0 4206 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-5 1886  ax-6 1945  ax-7 1990  ax-8 2081  ax-9 2089  ax-10 2110  ax-11 2124  ax-12 2139  ax-ext 2767 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1523  df-ex 1760  df-nf 1764  df-sb 2041  df-clab 2774  df-cleq 2786  df-clel 2861  df-nfc 2933  df-v 3434  df-dif 3857  df-un 3859  df-in 3861  df-ss 3869  df-symdif 4134  df-nul 4207 This theorem is referenced by: (None)
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