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Theorem difundi 3722
 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 3708 . . 3
21difeq2i 3577 . 2
3 inindi 3676 . . 3
4 dfin2 3706 . . 3
5 invdif 3711 . . . 4
6 invdif 3711 . . . 4
75, 6ineq12i 3659 . . 3
83, 4, 73eqtr3i 2457 . 2
92, 8eqtri 2449 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  cvv 3078   cdif 3430   cun 3431   cin 3432 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 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440 This theorem is referenced by:  undm  3728  uncld  20033  inmbl  22472  difuncomp  28146  clsun  30970  poimirlem8  31856
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