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Theorem ssun3 3340
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 3338 . 2  |-  B  C_  ( B  u.  C
)
2 sstr2 3186 . 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 3150    C_ wss 3152
This theorem is referenced by:  ssun  3354  ssunsn2  3773  pwundifOLD  4301  xpsspw  4797  xpsspwOLD  4798  uncmp  17130  alexsubALTlem3  17743  wfrlem15  24270  altxpsspw  24511  bnj1450  29080
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166
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