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Theorem ssun4 3499
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
StepHypRef Expression
1 ssun2 3497 . 2  |-  B  C_  ( C  u.  B
)
2 sstr2 3341 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( C  u.  B )  ->  A  C_  ( C  u.  B
) ) )
31, 2mpi 17 1  |-  ( A 
C_  B  ->  A  C_  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    u. cun 3304    C_ wss 3306
This theorem is referenced by:  ssun  3512  xpsspw  5015  xpsspwOLD  5016  uncmp  17497  volcn  19529  dftrpred3g  25542  elrfi  26786  bnj1408  29503  bnj1452  29519
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2964  df-un 3311  df-in 3313  df-ss 3320
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