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Theorem difindi 3587
 Description: Distributive law for class difference. Theorem 40 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
difindi

Proof of Theorem difindi
StepHypRef Expression
1 dfin3 3572 . . 3
21difeq2i 3454 . 2
3 indi 3579 . . 3
4 dfin2 3569 . . 3
5 invdif 3574 . . . 4
6 invdif 3574 . . . 4
75, 6uneq12i 3491 . . 3
83, 4, 73eqtr3i 2463 . 2
92, 8eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  cvv 2948   cdif 3309   cun 3310   cin 3311 This theorem is referenced by:  difdif2  3590  indm  3592  dprddisj2  15589  fctop  17060  cctop  17062  mretopd  17148  restcld  17228  cfinfil  17917  csdfil  17918  fndifnfp  26728 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319
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