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Theorem drsprs 14386
 Description: A directed set is a preset. (Contributed by Stefan O'Rear, 1-Feb-2015.)
Assertion
Ref Expression
drsprs Dirset

Proof of Theorem drsprs
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . . 3
2 eqid 2436 . . 3
31, 2isdrs 14384 . 2 Dirset
43simp1bi 972 1 Dirset
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725   wne 2599  wral 2698  wrex 2699  c0 3621   class class class wbr 4205  cfv 5447  cbs 13462  cple 13529   cpreset 14376  Dirsetcdrs 14377 This theorem is referenced by:  drsdirfi  14388  isdrs2  14389 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4331 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-sbc 3155  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-iota 5411  df-fv 5455  df-drs 14379
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