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Theorem ssun3 3205
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 3203 . 2  |-  B  C_  ( B  u.  C
)
2 sstr2 3068 . 2  |-  ( A 
C_  B  ->  ( B  C_  ( B  u.  C )  ->  A  C_  ( B  u.  C
) ) )
31, 2mpi 15 1  |-  ( A 
C_  B  ->  A  C_  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    u. cun 3033    C_ wss 3035
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-un 3039  df-in 3041  df-ss 3048
This theorem is referenced by:  ssun  3219  xpsspw  4609
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