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Theorem reltpos 7302
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 7301 . 2 tpos 𝐹 ⊆ ((dom 𝐹 ∪ {∅}) × ran 𝐹)
2 relxp 5188 . 2 Rel ((dom 𝐹 ∪ {∅}) × ran 𝐹)
3 relss 5167 . 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 3553  wss 3555  c0 3891  {csn 4148   × cxp 5072  ccnv 5073  dom cdm 5074  ran crn 5075  Rel wrel 5079  tpos ctpos 7296
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-rab 2916  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-br 4614  df-opab 4674  df-mpt 4675  df-xp 5080  df-rel 5081  df-cnv 5082  df-co 5083  df-dm 5084  df-rn 5085  df-res 5086  df-ima 5087  df-tpos 7297
This theorem is referenced by:  brtpos2  7303  relbrtpos  7308  dftpos2  7314  dftpos3  7315  tpostpos  7317
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