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Theorem relsn2m 5004
 Description: A singleton is a relation iff it has an inhabited domain. (Contributed by Jim Kingdon, 16-Dec-2018.)
Hypothesis
Ref Expression
relsn2m.1
Assertion
Ref Expression
relsn2m
Distinct variable group:   ,

Proof of Theorem relsn2m
StepHypRef Expression
1 relsn2m.1 . . 3
21relsn 4639 . 2
3 dmsnm 4999 . 2
42, 3bitri 183 1
 Colors of variables: wff set class Syntax hints:   wb 104  wex 1468   wcel 1480  cvv 2681  csn 3522   cxp 4532   cdm 4534   wrel 4539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-xp 4540  df-rel 4541  df-dm 4544 This theorem is referenced by: (None)
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