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Theorem relsnop 5009
 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 4953 . 2
4 opex 4456 . . 3
54relsn 5008 . 2
63, 5mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wcel 1727  cvv 2962  csn 3838  cop 3841   cxp 4905   wrel 4912 This theorem is referenced by:  cnvsn  5381  fsn  5935  imasaddfnlem  13784  ex-res  21780 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 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-opab 4292  df-xp 4913  df-rel 4914
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