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Theorem unss12 3279
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 3276 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
2 unss2 3278 . 2 (𝐶𝐷 → (𝐵𝐶) ⊆ (𝐵𝐷))
31, 2sylan9ss 3141 1 ((𝐴𝐵𝐶𝐷) → (𝐴𝐶) ⊆ (𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  cun 3100  wss 3102
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-in 3108  df-ss 3115
This theorem is referenced by:  ifssun  3519  fun  5342  resasplitss  5349
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