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Theorem snsstp1 3555
Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.)
Assertion
Ref Expression
snsstp1  |-  { A }  C_  { A ,  B ,  C }

Proof of Theorem snsstp1
StepHypRef Expression
1 snsspr1 3553 . . 3  |-  { A }  C_  { A ,  B }
2 ssun1 3145 . . 3  |-  { A ,  B }  C_  ( { A ,  B }  u.  { C } )
31, 2sstri 3017 . 2  |-  { A }  C_  ( { A ,  B }  u.  { C } )
4 df-tp 3424 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
53, 4sseqtr4i 3041 1  |-  { A }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    u. cun 2980    C_ wss 2982   {csn 3416   {cpr 3417   {ctp 3418
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pr 3423  df-tp 3424
This theorem is referenced by: (None)
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