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Theorem relsnop 4444
 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 4390 . 2
4 opexgOLD 3965 . . . 4
51, 2, 4mp2an 402 . . 3
65relsn 4443 . 2
73, 6mpbir 134 1
 Colors of variables: wff set class Syntax hints:   wcel 1393  cvv 2557  csn 3375  cop 3378   cxp 4343   wrel 4350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819  df-xp 4351  df-rel 4352 This theorem is referenced by:  cnvsn  4803  fsn  5335
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