Theorem snsspr1 4179

Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004.)

Assertion

Ref	Expression
snsspr1

Proof of Theorem snsspr1

Step	Hyp	Ref	Expression
1		ssun1 3666	. 2
2		df-pr 4032	. 2
3	1, 2	sseqtr4i 3536	1

Syntax hints:  u.cun 3473  C_wss 3475  {csn 4029  {cpr 4031

This theorem is referenced by:  snsstp1  4181  op1stb  4722  uniop  4755  rankopb  8291  ltrelxr  9669  2strbas  14734  phlvsca  14782  prdshom  14864  ipobas  15785  ipolerval  15786  lspprid1  17643  lsppratlem3  17795  lsppratlem4  17796  constr3pthlem1  24655  ex-dif  25144  ex-un  25145  ex-in  25146  coinflippv  28422  subfacp1lem2a  28624  altopthsn  29611  rankaltopb  29629  algsca  31130  gsumpr  32950  dvh3dim3N  37176  mapdindp2  37448  lspindp5  37497

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-pr 4032