Theorem inabs 2823

Description: Absorption law for intersection.

Assertion

Ref	Expression
inabs	|- (A i^i (A u. B)) = A

Proof of Theorem inabs

Step	Hyp	Ref	Expression
1		ssun1 2767	. 2 |- A C_ (A u. B)
2		df-ss 2605	. 2 |- (A C_ (A u. B) <-> (A i^i (A u. B)) = A)
3	1, 2	mpbi 206	1 |- (A i^i (A u. B)) = A

Syntax hints:   = wceq 1298   u. cun 2591   i^i cin 2592   C_ wss 2593

This theorem is referenced by:  inundifOLD 2952

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294  df-un 2600  df-in 2603  df-ss 2605

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