Theorem ssun3 3205

Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
ssun3	|- ( A C_ B -> A C_ ( B u. C ) )

Proof of Theorem ssun3

Step	Hyp	Ref	Expression
1		ssun1 3203	. 2 |- B C_ ( B u. C )
2		sstr2 3068	. 2 |- ( A C_ B -> ( B C_ ( B u. C ) -> A C_ ( B u. C ) ) )
3	1, 2	mpi 15	1 |- ( A C_ B -> A C_ ( B u. C ) )

Syntax hints:   -> wi 4   u. cun 3033   C_ wss 3035

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-un 3039  df-in 3041  df-ss 3048

This theorem is referenced by:  ssun  3219  xpsspw  4609