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Theorem reltpos 6255
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 6254 . 2  |- tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )
2 relxp 4810 . 2  |-  Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )
3 relss 4791 . 2  |-  (tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )  ->  ( Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )  ->  Rel tpos  F ) )
41, 2, 3mp2 17 1  |-  Rel tpos  F
Colors of variables: wff set class
Syntax hints:    u. cun 3163    C_ wss 3165   (/)c0 3468   {csn 3653    X. cxp 4703   `'ccnv 4704   dom cdm 4705   ran crn 4706   Rel wrel 4710  tpos ctpos 6249
This theorem is referenced by:  brtpos2  6256  relbrtpos  6261  dftpos2  6267  dftpos3  6268  tpostpos  6270
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-mpt 4095  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-tpos 6250
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