Theorem ssun4 3779

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 3777	. 2 |- B C_ ( C u. B )
2		sstr2 3610	. 2 |- ( A C_ B -> ( B C_ ( C u. B ) -> A C_ ( C u. B ) ) )
3	1, 2	mpi 20	1 |- ( A C_ B -> A C_ ( C u. B ) )

Syntax hints:   -> wi 4   u. cun 3572   C_ wss 3574

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-in 3581  df-ss 3588

This theorem is referenced by:  ssun  3792  xpsspw  5233  uncmp  21206  volcn  23374  bnj1408  31104  bnj1452  31120  dftrpred3g  31733  elrfi  37257  cnvrcl0  37932