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Theorem ssun 4182
Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
ssun ((𝐴𝐵𝐴𝐶) → 𝐴 ⊆ (𝐵𝐶))

Proof of Theorem ssun
StepHypRef Expression
1 ssun3 4167 . 2 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
2 ssun4 4168 . 2 (𝐴𝐶𝐴 ⊆ (𝐵𝐶))
31, 2jaoi 854 1 ((𝐴𝐵𝐴𝐶) → 𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 844  cun 3939  wss 3941
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-in 3948  df-ss 3958
This theorem is referenced by:  pwssun  5562  ordssun  6457  padct  32416
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