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Theorem unss12 3435
 Description: Subclass law for union of classes. (Contributed by NM, 2-Jun-2004.)
Assertion
Ref Expression
unss12 ((A B C D) → (AC) (BD))

Proof of Theorem unss12
StepHypRef Expression
1 unss1 3432 . 2 (A B → (AC) (BC))
2 unss2 3434 . 2 (C D → (BC) (BD))
31, 2sylan9ss 3285 1 ((A B C D) → (AC) (BD))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∪ 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:  fun  5236
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