Theorem snsstp3 4183

Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013.)

Assertion

Ref	Expression
snsstp3

Proof of Theorem snsstp3

Step	Hyp	Ref	Expression
1		ssun2 3667	. 2
2		df-tp 4034	. 2
3	1, 2	sseqtr4i 3536	1

Syntax hints:  u.cun 3473  C_wss 3475  {csn 4029  {cpr 4031  {ctp 4033

This theorem is referenced by:  fr3nr  6615  rngmulr  14747  srngmulr  14755  lmodsca  14764  ipsmulr  14771  ipsip  14774  phlsca  14781  topgrptset  14789  otpsle  14796  odrngmulr  14807  odrngds  14810  prdsmulr  14856  prdsip  14858  prdsds  14861  imasds  14910  imasmulr  14915  imasip  14918  fuccofval  15328  setccofval  15409  catccofval  15427  xpccofval  15451  psrmulr  18037  cnfldmul  18426  cnfldds  18430  trkgitv  23843  signswch  28518  algmulr  31129  estrccofval  32635  rngccofvalOLD  32795  ringccofvalOLD  32858

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-tp 4034