Theorem inabs 2235

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 2189	. 2 |- A (_ (A u. B)
2		df-ss 2049	. 2 |- (A (_ (A u. B) <-> (A i^i (A u. B)) = A)
3	1, 2	mpbi 189	1 |- (A i^i (A u. B)) = A

Syntax hints:   = wceq 954   u. cun 2041   i^i cin 2042   (_ wss 2043

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-un 2046  df-in 2047  df-ss 2049

Copyright terms: Public domain