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Theorem ssun3 4174
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 4172 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 3987 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3945  wss 3947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-un 3952  df-in 3954  df-ss 3964
This theorem is referenced by:  ssun  4189  ssunsn2  4831  xpsspw  5811  wfrlem15OLD  8344  uncmp  23320  alexsubALTlem3  23966  sxbrsigalem0  33891  bnj1450  34681  fineqvac  34717  altxpsspw  35573  pibt2  36896  superuncl  42998  cnvtrcl0  43056
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