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Theorem ssun3 3921
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 3919 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 3751 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cun 3713  wss 3715
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720  df-in 3722  df-ss 3729
This theorem is referenced by:  ssun  3935  ssunsn2  4504  xpsspw  5389  wfrlem15  7598  uncmp  21408  alexsubALTlem3  22054  sxbrsigalem0  30642  bnj1450  31425  altxpsspw  32390  superuncl  38375  cnvtrcl0  38435
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