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Theorem symdif1 3280
 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 3268 . 2
2 difin 3252 . . 3
3 incom 3207 . . . . 5
43difeq2i 3130 . . . 4
5 difin 3252 . . . 4
64, 5eqtri 2115 . . 3
72, 6uneq12i 3167 . 2
81, 7eqtr2i 2116 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   cdif 3010   cun 3011   cin 3012 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-fal 1302  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rab 2379  df-v 2635  df-dif 3015  df-un 3017  df-in 3019 This theorem is referenced by: (None)
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