Theorem relsn 5111

Description: A singleton is a relation iff it is an ordered pair. (Contributed by NM, 24-Sep-2013.)

Hypothesis

Ref	Expression
relsn.1

Assertion

Ref	Expression
relsn

Proof of Theorem relsn

Step	Hyp	Ref	Expression
1		df-rel 5011	. 2
2		relsn.1	. . 3
3	2	snss 4154	. 2
4	1, 3	bitr4i 252	1

Syntax hints:  <->wb 184  e.wcel 1818  cvv 3109  C_wss 3475  {csn 4029  X.cxp 5002  Relwrel 5009

This theorem is referenced by:  relsnop  5112  relsn2  5483  setscom  14662  setsid  14673

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-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-in 3482  df-ss 3489  df-sn 4030  df-rel 5011