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Theorem ex-ss 27414
 Description: Example for df-ss 3621. 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 3809 . 2 {1, 2} ⊆ ({1, 2} ∪ {3})
2 df-tp 4215 . 2 {1, 2, 3} = ({1, 2} ∪ {3})
31, 2sseqtr4i 3671 1 {1, 2} ⊆ {1, 2, 3}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3605   ⊆ wss 3607  {csn 4210  {cpr 4212  {ctp 4214  1c1 9975  2c2 11108  3c3 11109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-in 3614  df-ss 3621  df-tp 4215 This theorem is referenced by:  ex-pss  27415
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