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Theorem ssun 4189
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 4174 . 2 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
2 ssun4 4175 . 2 (𝐴𝐶𝐴 ⊆ (𝐵𝐶))
31, 2jaoi 855 1 ((𝐴𝐵𝐴𝐶) → 𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 845  cun 3946  wss 3948
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-un 3953  df-in 3955  df-ss 3965
This theorem is referenced by:  pwssun  5571  ordssun  6466  padct  31939
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