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Theorem reldir 15990
 Description: A direction is a relation. (Contributed by Jeff Hankins, 25-Nov-2009.) (Revised by Mario Carneiro, 22-Nov-2013.)
Assertion
Ref Expression
reldir

Proof of Theorem reldir
StepHypRef Expression
1 eqid 2457 . . . 4
21isdir 15989 . . 3
32ibi 241 . 2
43simplld 754 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wcel 1819   wss 3471  cuni 4251   cid 4799   cxp 5006  ccnv 5007   cres 5010   ccom 5012   wrel 5013  cdir 15985 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-in 3478  df-ss 3485  df-uni 4252  df-br 4457  df-opab 4516  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-res 5020  df-dir 15987 This theorem is referenced by:  dirtr  15993  dirge  15994
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