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Theorem posispre 25241
Description: A poset is a preset. (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
posispre  |-  ( A  e.  PosetRel  ->  A  e. PresetRel )

Proof of Theorem posispre
StepHypRef Expression
1 posprsr 25240 . 2  |-  PosetRel  C_ PresetRel
21sseli 3176 1  |-  ( A  e.  PosetRel  ->  A  e. PresetRel )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   PosetRelcps 14301  PresetRelcpresetrel 25215
This theorem is referenced by:  sege  25252  defse3  25272  supaub  25273  supwlub  25274  geme2  25275  tolat  25286  latdir  25295
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-ps 14306  df-prs 25223
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