Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  difundi Unicode version

Theorem difundi 3421
 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 3407 . . 3
21difeq2i 3291 . 2
3 inindi 3386 . . 3
4 dfin2 3405 . . 3
5 invdif 3410 . . . 4
6 invdif 3410 . . . 4
75, 6ineq12i 3368 . . 3
83, 4, 73eqtr3i 2311 . 2
92, 8eqtri 2303 1
 Colors of variables: wff set class Syntax hints:   wceq 1623  cvv 2788   cdif 3149   cun 3150   cin 3151 This theorem is referenced by:  undm  3426  uncld  16778  inmbl  18899  clsun  26246 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159
 Copyright terms: Public domain W3C validator