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Theorem ssun4 3429
Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994.)
Assertion
Ref Expression
ssun4 (A BA (CB))

Proof of Theorem ssun4
StepHypRef Expression
1 ssun2 3427 . 2 B (CB)
2 sstr2 3279 . 2 (A B → (B (CB) → A (CB)))
31, 2mpi 16 1 (A BA (CB))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3207   wss 3257
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259
This theorem is referenced by:  ssun  3442
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