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Theorem difindir 3728
 Description: Distributive law for class difference. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
difindir

Proof of Theorem difindir
StepHypRef Expression
1 inindir 3680 . 2
2 invdif 3714 . 2
3 invdif 3714 . . 3
4 invdif 3714 . . 3
53, 4ineq12i 3662 . 2
61, 2, 53eqtr3i 2459 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  cvv 3081   cdif 3433   cin 3435 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rab 2784  df-v 3083  df-dif 3439  df-in 3443 This theorem is referenced by:  ablfac1eulem  17693  ballotlemgun  29353  ballotlemgunOLD  29391
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