Theorem unabs 2241

Description: Absorption law for union.

Assertion

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

Proof of Theorem unabs

Step	Hyp	Ref	Expression
1		inss1 2233	. 2 |- (A i^i B) (_ A
2		ssequn2 2206	. 2 |- ((A i^i B) (_ A <-> (A u. (A i^i B)) = A)
3	1, 2	mpbi 189	1 |- (A u. (A i^i B)) = A

Syntax hints:   = wceq 958   u. cun 2048   i^i cin 2049   (_ wss 2050

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-in 2054  df-ss 2056

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