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Theorem ssun4 3629
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 3627 . 2  |-  B  C_  ( C  u.  B
)
2 sstr2 3468 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( C  u.  B )  ->  A  C_  ( C  u.  B
) ) )
31, 2mpi 21 1  |-  ( A 
C_  B  ->  A  C_  ( C  u.  B
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    u. cun 3431    C_ wss 3433
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 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
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 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-v 3080  df-un 3438  df-in 3440  df-ss 3447
This theorem is referenced by:  ssun  3642  xpsspw  4959  uncmp  20342  volcn  22458  bnj1408  29659  bnj1452  29675  dftrpred3g  30287  elrfi  35274
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