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Theorem ssun3 4101
 Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ssun3 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))

Proof of Theorem ssun3
StepHypRef Expression
1 ssun1 4099 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 3922 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∪ cun 3879   ⊆ wss 3881 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898 This theorem is referenced by:  ssun  4116  ssunsn2  4720  xpsspw  5646  wfrlem15  7952  uncmp  22008  alexsubALTlem3  22654  sxbrsigalem0  31639  bnj1450  32432  altxpsspw  33551  pibt2  34834  superuncl  40265  cnvtrcl0  40324
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