MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ex-ss Structured version   Unicode version

Theorem ex-ss 21740
Description: Example for df-ss 3336. 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 3512 . 2  |-  { 1 ,  2 }  C_  ( { 1 ,  2 }  u.  { 3 } )
2 df-tp 3824 . 2  |-  { 1 ,  2 ,  3 }  =  ( { 1 ,  2 }  u.  { 3 } )
31, 2sseqtr4i 3383 1  |-  { 1 ,  2 }  C_  { 1 ,  2 ,  3 }
Colors of variables: wff set class
Syntax hints:    u. cun 3320    C_ wss 3322   {csn 3816   {cpr 3817   {ctp 3818   1c1 8996   2c2 10054   3c3 10055
This theorem is referenced by:  ex-pss  21741
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-tp 3824
  Copyright terms: Public domain W3C validator