Theorem unabs 3307

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

Assertion

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

Proof of Theorem unabs

Step	Hyp	Ref	Expression
1		inss1 3296	. 2 |- ( A i^i B ) C_ A
2		ssequn2 3249	. 2 |- ( ( A i^i B ) C_ A <-> ( A u. ( A i^i B ) ) = A )
3	1, 2	mpbi 144	1 |- ( A u. ( A i^i B ) ) = A

Syntax hints:   = wceq 1331   u. cun 3069   i^i cin 3070   C_ wss 3071

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084

This theorem is referenced by: (None)