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Theorem reltpos 6476
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 6475 . 2  |- tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )
2 relxp 4975 . 2  |-  Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )
3 relss 4955 . 2  |-  (tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )  ->  ( Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )  ->  Rel tpos  F ) )
41, 2, 3mp2 9 1  |-  Rel tpos  F
Colors of variables: wff set class
Syntax hints:    u. cun 3310    C_ wss 3312   (/)c0 3620   {csn 3806    X. cxp 4868   `'ccnv 4869   dom cdm 4870   ran crn 4871   Rel wrel 4875  tpos ctpos 6470
This theorem is referenced by:  brtpos2  6477  relbrtpos  6482  dftpos2  6488  dftpos3  6489  tpostpos  6491
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-mpt 4260  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-tpos 6471
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