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Theorem ssun4 3167
Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994.)
Assertion
Ref Expression
ssun4 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))

Proof of Theorem ssun4
StepHypRef Expression
1 ssun2 3165 . 2 𝐵 ⊆ (𝐶𝐵)
2 sstr2 3033 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐶𝐵) → 𝐴 ⊆ (𝐶𝐵)))
31, 2mpi 15 1 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4  cun 2998  wss 3000
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-un 3004  df-in 3006  df-ss 3013
This theorem is referenced by:  ssun  3180  xpsspw  4563
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