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Theorem ex-ss 26438
 Description: Example for df-ss 3549. 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 3733 . 2 {1, 2} ⊆ ({1, 2} ∪ {3})
2 df-tp 4125 . 2 {1, 2, 3} = ({1, 2} ∪ {3})
31, 2sseqtr4i 3596 1 {1, 2} ⊆ {1, 2, 3}
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3533   ⊆ wss 3535  {csn 4120  {cpr 4122  {ctp 4124  1c1 9789  2c2 10913  3c3 10914 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2228  ax-ext 2585 This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-nfc 2735  df-v 3170  df-un 3540  df-in 3542  df-ss 3549  df-tp 4125 This theorem is referenced by:  ex-pss  26439
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