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Theorem reltpos 6853
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 6852 . 2  |- tpos  F  C_  ( ( `' dom  F  u.  { (/) } )  X.  ran  F )
2 relxp 5048 . 2  |-  Rel  (
( `' dom  F  u.  { (/) } )  X. 
ran  F )
3 relss 5028 . 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 setvar class
Syntax hints:    u. cun 3427    C_ wss 3429   (/)c0 3738   {csn 3978    X. cxp 4939   `'ccnv 4940   dom cdm 4941   ran crn 4942   Rel wrel 4946  tpos ctpos 6847
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4514  ax-nul 4522  ax-pr 4632
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3073  df-dif 3432  df-un 3434  df-in 3436  df-ss 3443  df-nul 3739  df-if 3893  df-sn 3979  df-pr 3981  df-op 3985  df-br 4394  df-opab 4452  df-mpt 4453  df-xp 4947  df-rel 4948  df-cnv 4949  df-co 4950  df-dm 4951  df-rn 4952  df-res 4953  df-ima 4954  df-tpos 6848
This theorem is referenced by:  brtpos2  6854  relbrtpos  6859  dftpos2  6865  dftpos3  6866  tpostpos  6868
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