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Theorem symdif1 3433
 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 3422 . 2
2 difin 3406 . . 3
3 incom 3361 . . . . 5
43difeq2i 3291 . . . 4
5 difin 3406 . . . 4
64, 5eqtri 2303 . . 3
72, 6uneq12i 3327 . 2
81, 7eqtr2i 2304 1
 Colors of variables: wff set class Syntax hints:   wceq 1623   cdif 3149   cun 3150   cin 3151 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159
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