Theorem ssun2 2184

Description: Subclass relationship for union of classes.

Assertion

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

Proof of Theorem ssun2

Step	Hyp	Ref	Expression
1		ssun1 2183	. 2 |- A (_ (A u. B)
2		uncom 2166	. 2 |- (A u. B) = (B u. A)
3	1, 2	sseqtr 2083	1 |- A (_ (B u. A)

Syntax hints:   u. cun 2035   (_ wss 2037

This theorem is referenced by:  ssun4 2186  elun2 2188  nsspssun 2231  unv 2290  un00 2296  unexb 2864  difex2 2867  rnexg 3345  mapunen 4482  trcl 4617  rankun 4663  alephfplem4 4871  cfsuc 4887  infxpidmlem12 7506  psdmrn 8574  shlub 9261  shsumval2 9275  sshhococ 9384

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-un 2040  df-in 2041  df-ss 2043

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