Theorem inindir 3715

Description: Intersection distributes over itself. (Contributed by NM, 17-Aug-2004.)

Assertion

Ref	Expression
inindir

Proof of Theorem inindir

Step	Hyp	Ref	Expression
1		inidm 3706	. . 3
2	1	ineq2i 3696	. 2
3		in4 3713	. 2
4	2, 3	eqtr3i 2488	1

Syntax hints:  =wceq 1395  i^icin 3474

This theorem is referenced by:  difindir  3752  resindir  5295  restbas  19659  consuba  19921  kgentopon  20039  trfbas2  20344  trfil2  20388  fclsrest  20525  trust  20732  chtdif  23432  ppidif  23437  mdslmd1lem1  27244  mdslmd1lem2  27245  mddmdin0i  27350  ballotlemgun  28463  cvmsss2  28719  predin  29269

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-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-v 3111  df-in 3482