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Theorem unss12 3818
Description: Subclass law for union of classes. (Contributed by NM, 2-Jun-2004.)
Assertion
Ref Expression
unss12 ((𝐴𝐵𝐶𝐷) → (𝐴𝐶) ⊆ (𝐵𝐷))

Proof of Theorem unss12
StepHypRef Expression
1 unss1 3815 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
2 unss2 3817 . 2 (𝐶𝐷 → (𝐵𝐶) ⊆ (𝐵𝐷))
31, 2sylan9ss 3649 1 ((𝐴𝐵𝐶𝐷) → (𝐴𝐶) ⊆ (𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  cun 3605  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-in 3614  df-ss 3621
This theorem is referenced by:  pwssun  5049  fun  6104  undom  8089  finsschain  8314  trclun  13799  relexpfld  13833  mvdco  17911  dprd2da  18487  dmdprdsplit2lem  18490  lspun  19035  spanuni  28531  sshhococi  28533  mthmpps  31605  mblfinlem3  33578  dochdmj1  36996  mptrcllem  38237  clcnvlem  38247  dfrcl2  38283  relexpss1d  38314  corclrcl  38316  relexp0a  38325  corcltrcl  38348  frege131d  38373
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