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Theorem ssun 3442
 Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
ssun ((A B A C) → A (BC))

Proof of Theorem ssun
StepHypRef Expression
1 ssun3 3428 . 2 (A BA (BC))
2 ssun4 3429 . 2 (A CA (BC))
31, 2jaoi 368 1 ((A B A C) → A (BC))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   ∪ cun 3207   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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: (None)
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