Theorem ssun4 3299

Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994.)

Assertion

Ref	Expression
ssun4	|- ( A C_ B -> A C_ ( C u. B ) )

Proof of Theorem ssun4

Step	Hyp	Ref	Expression
1		ssun2 3297	. 2 |- B C_ ( C u. B )
2		sstr2 3160	. 2 |- ( A C_ B -> ( B C_ ( C u. B ) -> A C_ ( C u. B ) ) )
3	1, 2	mpi 15	1 |- ( A C_ B -> A C_ ( C u. B ) )

Syntax hints:   -> wi 4   u. cun 3125   C_ wss 3127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-in 3133  df-ss 3140

This theorem is referenced by:  ssun  3312  xpsspw  4732