Theorem ssun4 3109

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 3107	. 2 |- B C_ ( C u. B )
2		sstr2 2952	. 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 2915   C_ wss 2917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931

This theorem is referenced by:  ssun  3122  xpsspw  4450