Theorem inabs 3728

Description: Absorption law for intersection. (Contributed by NM, 16-Apr-2006.)

Assertion

Ref	Expression
inabs

Proof of Theorem inabs

Step	Hyp	Ref	Expression
1		ssun1 3666	. 2
2		df-ss 3489	. 2
3	1, 2	mpbi 208	1

Syntax hints:  =wceq 1395  u.cun 3473  i^icin 3474  C_wss 3475

This theorem is referenced by:  dfif5  3957

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-v 3111  df-un 3480  df-in 3482  df-ss 3489