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Theorem symdif1 3394
 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 3383 . 2
2 difin 3367 . . 3
3 incom 3322 . . . . 5
43difeq2i 3252 . . . 4
5 difin 3367 . . . 4
64, 5eqtri 2276 . . 3
72, 6uneq12i 3288 . 2
81, 7eqtr2i 2277 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   cdif 3110   cun 3111   cin 3112 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ral 2521  df-rab 2525  df-v 2759  df-dif 3116  df-un 3118  df-in 3120
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