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Theorem snsspr2 3560
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
snsspr2  |-  { B }  C_  { A ,  B }

Proof of Theorem snsspr2
StepHypRef Expression
1 ssun2 3148 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3429 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3043 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 2982    C_ wss 2984   {csn 3422   {cpr 3423
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 2614  df-un 2988  df-in 2990  df-ss 2997  df-pr 3429
This theorem is referenced by:  snsstp2  3562  ssprr  3574  ord3ex  3989  ltrelxr  7450
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