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Theorem ssun4 3481
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 3479 . 2  |-  B  C_  ( C  u.  B
)
2 sstr2 3323 . 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 3286    C_ wss 3288
This theorem is referenced by:  ssun  3494  xpsspw  4953  xpsspwOLD  4954  uncmp  17428  volcn  19459  dftrpred3g  25458  elrfi  26646  bnj1408  29123  bnj1452  29139
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-in 3295  df-ss 3302
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