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Theorem reldir 14683
 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 2438 . . . . 5
21isdir 14682 . . . 4
32ibi 234 . . 3
43simpld 447 . 2
54simpld 447 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726   wss 3322  cuni 4017   cid 4496   cxp 4879  ccnv 4880   cres 4883   ccom 4885   wrel 4886  cdir 14678 This theorem is referenced by:  dirtr  14686  dirge  14687 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-uni 4018  df-br 4216  df-opab 4270  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-res 4893  df-dir 14680
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