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Theorem ssun3 3374
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 3372 . 2  |-  B  C_  ( B  u.  C
)
2 sstr2 3220 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( B  u.  C )  ->  A  C_  ( B  u.  C
) ) )
31, 2mpi 16 1  |-  ( A 
C_  B  ->  A  C_  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    u. cun 3184    C_ wss 3186
This theorem is referenced by:  ssun  3388  ssunsn2  3810  pwundifOLD  4338  xpsspw  4834  xpsspwOLD  4835  uncmp  17186  alexsubALTlem3  17795  sxbrsigalem0  23795  wfrlem15  24655  altxpsspw  24897  bnj1450  28591
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-un 3191  df-in 3193  df-ss 3200
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