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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
StepHypRef Expression
1 df-rel 5011 . 2
2 relsn.1 . . 3
32snss 4154 . 2
41, 3bitr4i 252 1
 Colors of variables: wff setvar class 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
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