Theorem ssun2 1622

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 1621	. 2 |- A (_ (A u. B)
2		uncom 1604	. 2 |- (A u. B) = (B u. A)
3	1, 2	sseqtr 1532	1 |- A (_ (B u. A)

Syntax hints:   u. cun 1485   (_ wss 1487

This theorem is referenced by:  ssun4 1624  elun2 1626  nsspssun 1666  unv 1724  un00 1728  unexb 1950  difex2 1951  mapunen 3397  trcl 3489  rankun 3535  cfsuc 3709  infxpidmlem12 4944  shlub 5347  shsumval2 5361  sshhococ 5451

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-in 1491  df-ss 1492

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