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Theorem ssun3 4147
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 4145 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 3971 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3931  wss 3933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-un 3938  df-in 3940  df-ss 3949
This theorem is referenced by:  ssun  4162  ssunsn2  4752  xpsspw  5675  wfrlem15  7958  uncmp  21939  alexsubALTlem3  22585  sxbrsigalem0  31428  bnj1450  32219  altxpsspw  33335  pibt2  34580  superuncl  39805  cnvtrcl0  39864
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