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Theorem ssun 3099
 Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
ssun ((AB A𝐶) → A ⊆ (B𝐶))

Proof of Theorem ssun
StepHypRef Expression
1 ssun3 3085 . 2 (ABA ⊆ (B𝐶))
2 ssun4 3086 . 2 (A𝐶A ⊆ (B𝐶))
31, 2jaoi 623 1 ((AB A𝐶) → A ⊆ (B𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 616   ∪ cun 2892   ⊆ wss 2894 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899  df-in 2901  df-ss 2908 This theorem is referenced by:  pwunss  3994  pwssunim  3995
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