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Theorem elsn 3543
 Description: There is exactly one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. (Contributed by NM, 13-Sep-1995.)
Hypothesis
Ref Expression
elsn.1
Assertion
Ref Expression
elsn

Proof of Theorem elsn
StepHypRef Expression
1 elsn.1 . 2
2 elsng 3542 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331   wcel 1480  cvv 2686  csn 3527 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-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sn 3533 This theorem is referenced by:  velsn  3544  sneqr  3687  onsucelsucexmid  4445  ordsoexmid  4477  opthprc  4590  dmsnm  5004  dmsnopg  5010  cnvcnvsn  5015  sniota  5115  fsn  5592  eusvobj2  5760  mapdm0  6557  djulclb  6940  opelreal  7635
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