Theorem ssun2 3428

Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)

Assertion

Ref	Expression
ssun2	|- A C_ (B u. A)

Proof of Theorem ssun2

Step	Hyp	Ref	Expression
1		ssun1 3427	. 2 |- A C_ (A u. B)
2		uncom 3409	. 2 |- (A u. B) = (B u. A)
3	1, 2	sseqtri 3304	1 |- A C_ (B u. A)

Syntax hints:   u. cun 3208   C_ wss 3258

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-un 3215  df-ss 3260

This theorem is referenced by:  ssun4  3430  elun2  3432  nsspssun  3489  unv  3579  un00  3587  snsspr2  3858  snsstp3  3861  unsneqsn  3888  pw1equn  4332  pw1eqadj  4333  nndisjeq  4430  sfinltfin  4536  vfinspss  4552  proj1op  4601  proj2op  4602  enadj  6061  ncdisjun  6137  ce0addcnnul  6180  sbthlem1  6204