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Theorem ssun3 3740
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 3738 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 3575 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3538  wss 3540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554
This theorem is referenced by:  ssun  3754  ssunsn2  4299  xpsspw  5156  wfrlem15  7316  uncmp  21016  alexsubALTlem3  21663  sxbrsigalem0  29660  bnj1450  30372  altxpsspw  31254  superuncl  36892  cnvtrcl0  36952
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