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Theorem reltpos 8255
Description: The transposition is a relation. (Contributed by Mario Carneiro, 10-Sep-2015.)
Assertion
Ref Expression
reltpos Rel tpos 𝐹

Proof of Theorem reltpos
StepHypRef Expression
1 tposssxp 8254 . 2 tpos 𝐹 ⊆ ((dom 𝐹 ∪ {∅}) × ran 𝐹)
2 relxp 5707 . 2 Rel ((dom 𝐹 ∪ {∅}) × ran 𝐹)
3 relss 5794 . 2 (tpos 𝐹 ⊆ ((dom 𝐹 ∪ {∅}) × ran 𝐹) → (Rel ((dom 𝐹 ∪ {∅}) × ran 𝐹) → Rel tpos 𝐹))
41, 2, 3mp2 9 1 Rel tpos 𝐹
Colors of variables: wff setvar class
Syntax hints:  cun 3961  wss 3963  c0 4339  {csn 4631   × cxp 5687  ccnv 5688  dom cdm 5689  ran crn 5690  Rel wrel 5694  tpos ctpos 8249
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-mpt 5232  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-tpos 8250
This theorem is referenced by:  brtpos2  8256  relbrtpos  8261  dftpos2  8267  dftpos3  8268  tpostpos  8270
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