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Theorem ssun4 3670
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 3668 . 2  |-  B  C_  ( C  u.  B
)
2 sstr2 3511 . 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 setvar class
Syntax hints:    -> wi 4    u. cun 3474    C_ wss 3476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481  df-in 3483  df-ss 3490
This theorem is referenced by:  ssun  3683  xpsspw  5116  xpsspwOLD  5117  uncmp  19709  volcn  21842  dftrpred3g  29169  elrfi  30457  bnj1408  33388  bnj1452  33404
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