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Theorem ex-ss 25353
Description: Example for df-ss 3475. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.)
Assertion
Ref Expression
ex-ss  |-  { 1 ,  2 }  C_  { 1 ,  2 ,  3 }

Proof of Theorem ex-ss
StepHypRef Expression
1 ssun1 3653 . 2  |-  { 1 ,  2 }  C_  ( { 1 ,  2 }  u.  { 3 } )
2 df-tp 4021 . 2  |-  { 1 ,  2 ,  3 }  =  ( { 1 ,  2 }  u.  { 3 } )
31, 2sseqtr4i 3522 1  |-  { 1 ,  2 }  C_  { 1 ,  2 ,  3 }
Colors of variables: wff setvar class
Syntax hints:    u. cun 3459    C_ wss 3461   {csn 4016   {cpr 4018   {ctp 4020   1c1 9482   2c2 10581   3c3 10582
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3108  df-un 3466  df-in 3468  df-ss 3475  df-tp 4021
This theorem is referenced by:  ex-pss  25354
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