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Theorem ssun4 3429
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 3427 . 2  |-  B  C_  ( C  u.  B
)
2 sstr2 3272 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( C  u.  B )  ->  A  C_  ( C  u.  B
) ) )
31, 2mpi 16 1  |-  ( A 
C_  B  ->  A  C_  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    u. cun 3236    C_ wss 3238
This theorem is referenced by:  ssun  3442  xpsspw  4900  xpsspwOLD  4901  uncmp  17347  volcn  19176  dftrpred3g  25062  elrfi  26360  bnj1408  28818  bnj1452  28834
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-v 2875  df-un 3243  df-in 3245  df-ss 3252
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