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Theorem difdifdir 3637
 Description: Distributive law for class difference. Exercise 4.8 of [Stoll] p. 16. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
difdifdir

Proof of Theorem difdifdir
StepHypRef Expression
1 dif32 3517 . . . . 5
2 invdif 3496 . . . . 5
31, 2eqtr4i 2376 . . . 4
4 un0 3575 . . . 4
53, 4eqtr4i 2376 . . 3
6 indi 3501 . . . 4
7 disjdif 3622 . . . . . 6
8 incom 3448 . . . . . 6
97, 8eqtr3i 2375 . . . . 5
109uneq2i 3415 . . . 4
116, 10eqtr4i 2376 . . 3
125, 11eqtr4i 2376 . 2
13 ddif 3398 . . . . 5
1413uneq2i 3415 . . . 4
15 indm 3513 . . . . 5
16 invdif 3496 . . . . . 6
1716difeq2i 3382 . . . . 5
1815, 17eqtr3i 2375 . . . 4
1914, 18eqtr3i 2375 . . 3
2019ineq2i 3454 . 2
21 invdif 3496 . 2
2212, 20, 213eqtri 2377 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cvv 2859   cdif 3206   cun 3207   cin 3208  c0 3550 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by: (None)
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