Theorem ssun2 2194

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 2193	. 2 |- A (_ (A u. B)
2		uncom 2176	. 2 |- (A u. B) = (B u. A)
3	1, 2	sseqtr 2093	1 |- A (_ (B u. A)

Syntax hints:   u. cun 2045   (_ wss 2047

This theorem is referenced by:  ssun4 2196  elun2 2198  nsspssun 2241  unv 2300  un00 2306  unexb 2873  difex2 2877  rnexg 3359  mapunen 4502  trcl 4645  rankun 4691  alephfplem4 4899  cfsuc 4915  infxpidmlem12 7563  psdmrn 8648  shlub 9346  shsumval2 9360  sshhococ 9469

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-in 2051  df-ss 2053

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