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Theorem symdif1 3763
 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 3751 . 2
2 difin 3735 . . 3
3 incom 3691 . . . . 5
43difeq2i 3619 . . . 4
5 difin 3735 . . . 4
64, 5eqtri 2496 . . 3
72, 6uneq12i 3656 . 2
81, 7eqtr2i 2497 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379   cdif 3473   cun 3474   cin 3475 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483 This theorem is referenced by: (None)
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