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Theorem ex-ss 26676
 Description: Example for df-ss 3554. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-ss {1, 2} ⊆ {1, 2, 3}

Proof of Theorem ex-ss
StepHypRef Expression
1 ssun1 3738 . 2 {1, 2} ⊆ ({1, 2} ∪ {3})
2 df-tp 4130 . 2 {1, 2, 3} = ({1, 2} ∪ {3})
31, 2sseqtr4i 3601 1 {1, 2} ⊆ {1, 2, 3}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3538   ⊆ wss 3540  {csn 4125  {cpr 4127  {ctp 4129  1c1 9816  2c2 10947  3c3 10948 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-tp 4130 This theorem is referenced by:  ex-pss  26677
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