Theorem ssun3 3236

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 3234	. 2 |- B C_ ( B u. C )
2		sstr2 3099	. 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 3064   C_ wss 3066

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079

This theorem is referenced by:  ssun  3250  xpsspw  4646