Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  snsspr2 Structured version   Unicode version

Theorem snsspr2 3940
 Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
snsspr2

Proof of Theorem snsspr2
StepHypRef Expression
1 ssun2 3503 . 2
2 df-pr 3813 . 2
31, 2sseqtr4i 3373 1
 Colors of variables: wff set class Syntax hints:   cun 3310   wss 3312  csn 3806  cpr 3807 This theorem is referenced by:  snsstp2  3942  ord3ex  4381  ltrelxr  9131  2strop  13559  algvsca  13595  phlip  13605  prdsvsca  13675  prdsco  13682  imasvsca  13738  ipotset  14575  lsppratlem4  16214  constr3pthlem1  21634  ex-res  21741  subfacp1lem2a  24858  dvh3dim3N  32184 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-in 3319  df-ss 3326  df-pr 3813
 Copyright terms: Public domain W3C validator