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Theorem drsbn0 14386
 Description: The base of a directed set is not empty. (Contributed by Stefan O'Rear, 1-Feb-2015.)
Hypothesis
Ref Expression
drsbn0.b
Assertion
Ref Expression
drsbn0 Dirset

Proof of Theorem drsbn0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 drsbn0.b . . 3
2 eqid 2435 . . 3
31, 2isdrs 14383 . 2 Dirset
43simp2bi 973 1 Dirset
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  c0 3620   class class class wbr 4204  cfv 5446  cbs 13461  cple 13528   cpreset 14375  Dirsetcdrs 14376 This theorem is referenced by:  drsdirfi  14387  isipodrs  14579 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 2416  ax-nul 4330 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 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-drs 14378
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