Theorem difundir 3750

Description: Distributive law for class difference. (Contributed by NM, 17-Aug-2004.)

Assertion

Ref	Expression
difundir

Proof of Theorem difundir

Step	Hyp	Ref	Expression
1		indir 3745	. 2
2		invdif 3738	. 2
3		invdif 3738	. . 3
4		invdif 3738	. . 3
5	3, 4	uneq12i 3655	. 2
6	1, 2, 5	3eqtr3i 2494	1

Syntax hints:  =wceq 1395  cvv 3109  \cdif 3472  u.cun 3473  i^icin 3474

This theorem is referenced by:  symdif1  3762  difun2  3907  diftpsn3  4168  strleun  14727  mreexmrid  15040  mreexexlem2d  15042  mvdco  16470  dprd2da  17091  dmdprdsplit2lem  17094  ablfac1eulem  17123  lbsextlem4  17807  opsrtoslem2  18149  nulmbl2  21947  uniioombllem3  21994  ex-dif  25144  imadifxp  27458  ballotlemfp1  28430  ballotlemgun  28463  onint1  29914  dvmptfprodlem  31741  fourierdlem102  31991  fourierdlem114  32003

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