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Theorem ssun 4195
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 4180 . 2 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
2 ssun4 4181 . 2 (𝐴𝐶𝐴 ⊆ (𝐵𝐶))
31, 2jaoi 858 1 ((𝐴𝐵𝐴𝐶) → 𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 848  cun 3949  wss 3951
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-ss 3968
This theorem is referenced by:  pwssun  5575  ordssun  6486  padct  32731
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