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Theorem reltpos 6420
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 6419 . 2  |- tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )
2 relxp 4923 . 2  |-  Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )
3 relss 4903 . 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 3261    C_ wss 3263   (/)c0 3571   {csn 3757    X. cxp 4816   `'ccnv 4817   dom cdm 4818   ran crn 4819   Rel wrel 4823  tpos ctpos 6414
This theorem is referenced by:  brtpos2  6421  relbrtpos  6426  dftpos2  6432  dftpos3  6433  tpostpos  6435
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-br 4154  df-opab 4208  df-mpt 4209  df-xp 4824  df-rel 4825  df-cnv 4826  df-co 4827  df-dm 4828  df-rn 4829  df-res 4830  df-ima 4831  df-tpos 6415
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