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Theorem ssun3 3637
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 3635 . 2  |-  B  C_  ( B  u.  C
)
2 sstr2 3477 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( B  u.  C )  ->  A  C_  ( B  u.  C
) ) )
31, 2mpi 21 1  |-  ( A 
C_  B  ->  A  C_  ( B  u.  C
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    u. cun 3440    C_ wss 3442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-un 3447  df-in 3449  df-ss 3456
This theorem is referenced by:  ssun  3651  ssunsn2  4162  xpsspw  4968  wfrlem15  7058  uncmp  20349  alexsubALTlem3  20995  sxbrsigalem0  28932  bnj1450  29647  altxpsspw  30529  superuncl  35870
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