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Theorem ex-ss 21696
Description: Example for df-ss 3302. 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 3478 . 2  |-  { 1 ,  2 }  C_  ( { 1 ,  2 }  u.  { 3 } )
2 df-tp 3790 . 2  |-  { 1 ,  2 ,  3 }  =  ( { 1 ,  2 }  u.  { 3 } )
31, 2sseqtr4i 3349 1  |-  { 1 ,  2 }  C_  { 1 ,  2 ,  3 }
Colors of variables: wff set class
Syntax hints:    u. cun 3286    C_ wss 3288   {csn 3782   {cpr 3783   {ctp 3784   1c1 8955   2c2 10013   3c3 10014
This theorem is referenced by:  ex-pss  21697
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-in 3295  df-ss 3302  df-tp 3790
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