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Theorem ex-ss 21246
Description: Example for df-ss 3252. 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 3426 . 2  |-  { 1 ,  2 }  C_  ( { 1 ,  2 }  u.  { 3 } )
2 df-tp 3737 . 2  |-  { 1 ,  2 ,  3 }  =  ( { 1 ,  2 }  u.  { 3 } )
31, 2sseqtr4i 3297 1  |-  { 1 ,  2 }  C_  { 1 ,  2 ,  3 }
Colors of variables: wff set class
Syntax hints:    u. cun 3236    C_ wss 3238   {csn 3729   {cpr 3730   {ctp 3731   1c1 8885   2c2 9942   3c3 9943
This theorem is referenced by:  ex-pss  21247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-v 2875  df-un 3243  df-in 3245  df-ss 3252  df-tp 3737
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