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Theorem symdif1 3762
Description: Two ways to express symmetric difference. This theorem shows the equivalence of the definition of symmetric difference in [Stoll] p. 13 and the restated definition in Example 4.1 of [Stoll] p. 262. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
symdif1

Proof of Theorem symdif1
StepHypRef Expression
1 difundir 3750 . 2
2 difin 3734 . . 3
3 incom 3690 . . . . 5
43difeq2i 3618 . . . 4
5 difin 3734 . . . 4
64, 5eqtri 2486 . . 3
72, 6uneq12i 3655 . 2
81, 7eqtr2i 2487 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  \cdif 3472  u.cun 3473  i^icin 3474
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482
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