Theorem unabs 3338

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 3327	. 2 |- ( A i^i B ) C_ A
2		ssequn2 3280	. 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 1335   u. cun 3100   i^i cin 3101   C_ wss 3102

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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-in 3108  df-ss 3115

This theorem is referenced by: (None)