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Theorem relsn 5014
 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 4920 . 2
2 relsn.1 . . 3
32snss 3955 . 2
41, 3bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wb 178   wcel 1728  cvv 2965   wss 3309  csn 3843   cxp 4911   wrel 4918 This theorem is referenced by:  relsnop  5015  relsn2  5375  setscom  13535  setsid  13546 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-v 2967  df-in 3316  df-ss 3323  df-sn 3849  df-rel 4920
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