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Theorem relsnop 4640
 Description: A singleton of an ordered pair is a relation. (Contributed by NM, 17-May-1998.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
relsn.1
relsnop.2
Assertion
Ref Expression
relsnop

Proof of Theorem relsnop
StepHypRef Expression
1 relsn.1 . . 3
2 relsnop.2 . . 3
31, 2opelvv 4584 . 2
41, 2opex 4146 . . 3
54relsn 4639 . 2
63, 5mpbir 145 1
 Colors of variables: wff set class Syntax hints:   wcel 1480  cvv 2681  csn 3522  cop 3525   cxp 4532   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-ral 2419  df-rex 2420  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-opab 3985  df-xp 4540  df-rel 4541 This theorem is referenced by:  cnvsn  5016  fsn  5585
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