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Theorem unss12 3331
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 3328 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
2 unss2 3330 . 2 (𝐶𝐷 → (𝐵𝐶) ⊆ (𝐵𝐷))
31, 2sylan9ss 3192 1 ((𝐴𝐵𝐶𝐷) → (𝐴𝐶) ⊆ (𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  cun 3151  wss 3153
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-in 3159  df-ss 3166
This theorem is referenced by:  ifssun  3571  fun  5426  resasplitss  5433  lspun  13898
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