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Theorem ssun3 3512
Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ssun3  |-  ( A 
C_  B  ->  A  C_  ( B  u.  C
) )

Proof of Theorem ssun3
StepHypRef Expression
1 ssun1 3510 . 2  |-  B  C_  ( B  u.  C
)
2 sstr2 3355 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( B  u.  C )  ->  A  C_  ( B  u.  C
) ) )
31, 2mpi 17 1  |-  ( A 
C_  B  ->  A  C_  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    u. cun 3318    C_ wss 3320
This theorem is referenced by:  ssun  3526  ssunsn2  3958  xpsspw  4986  xpsspwOLD  4987  uncmp  17466  alexsubALTlem3  18080  sxbrsigalem0  24621  wfrlem15  25552  altxpsspw  25822  bnj1450  29419
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-in 3327  df-ss 3334
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