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Theorem snsspr1 3949
Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.)
Assertion
Ref Expression
snsspr1  |-  { A }  C_  { A ,  B }

Proof of Theorem snsspr1
StepHypRef Expression
1 ssun1 3512 . 2  |-  { A }  C_  ( { A }  u.  { B } )
2 df-pr 3823 . 2  |-  { A ,  B }  =  ( { A }  u.  { B } )
31, 2sseqtr4i 3383 1  |-  { A }  C_  { A ,  B }
Colors of variables: wff set class
Syntax hints:    u. cun 3320    C_ wss 3322   {csn 3816   {cpr 3817
This theorem is referenced by:  snsstp1  3951  uniop  4461  op1stb  4760  rankopb  7780  ltrelxr  9141  2strbas  13568  algsca  13604  phlvsca  13614  prdssca  13681  prdshom  13691  imassca  13747  ipobas  14583  ipolerval  14584  lspprid1  16075  lsppratlem3  16223  lsppratlem4  16224  constr3pthlem1  21644  ex-dif  21733  ex-un  21734  ex-in  21735  coinflippv  24743  subfacp1lem2a  24868  altopthsn  25808  rankaltopb  25826  dvh3dim3N  32309  mapdindp2  32581  lspindp5  32630
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-pr 3823
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