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Theorem difundi 3749
 Description: Distributive law for class difference. Theorem 39 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
difundi

Proof of Theorem difundi
StepHypRef Expression
1 dfun3 3735 . . 3
21difeq2i 3618 . 2
3 inindi 3714 . . 3
4 dfin2 3733 . . 3
5 invdif 3738 . . . 4
6 invdif 3738 . . . 4
75, 6ineq12i 3697 . . 3
83, 4, 73eqtr3i 2494 . 2
92, 8eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395   cvv 3109  \cdif 3472  u.cun 3473  i^icin 3474 This theorem is referenced by:  undm  3755  uncld  19542  inmbl  21952  clsun  30146 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482
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