Users' Mathboxes Mathbox for Frédéric Liné < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  posispre Unicode version

Theorem posispre 25344
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 25343 . 2  |-  PosetRel  C_ PresetRel
21sseli 3189 1  |-  ( A  e.  PosetRel  ->  A  e. PresetRel )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   PosetRelcps 14317  PresetRelcpresetrel 25318
This theorem is referenced by:  sege  25355  defse3  25375  supaub  25376  supwlub  25377  geme2  25378  tolat  25389  latdir  25398
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-ps 14322  df-prs 25326
  Copyright terms: Public domain W3C validator