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Theorem snsspr2 3765
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 3339 . 2  |-  { B }  C_  ( { A }  u.  { B } )
2 df-pr 3647 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3211 1  |-  { B }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3150    C_ wss 3152   {csn 3640   {cpr 3641
This theorem is referenced by:  snsstp2  3767  ord3ex  4200  ltrelxr  8886  2strop  13246  algvsca  13282  phlip  13292  prdsvsca  13360  prdsco  13367  imasvsca  13423  ipotset  14260  lsppratlem4  15903  ex-res  20828  subfacp1lem2a  23711  dvh3dim3N  31639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166  df-pr 3647
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