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Theorem ex-ss 28212
 Description: Example for df-ss 3898. 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 4099 . 2 {1, 2} ⊆ ({1, 2} ∪ {3})
2 df-tp 4530 . 2 {1, 2, 3} = ({1, 2} ∪ {3})
31, 2sseqtrri 3952 1 {1, 2} ⊆ {1, 2, 3}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3879   ⊆ wss 3881  {csn 4525  {cpr 4527  {ctp 4529  1c1 10527  2c2 11680  3c3 11681 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-tp 4530 This theorem is referenced by:  ex-pss  28213
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