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Theorem posprsr 25343
 Description: A partial order is a preset. (Contributed by FL, 1-May-2011.)
Assertion
Ref Expression
posprsr PresetRel

Proof of Theorem posprsr
StepHypRef Expression
1 inss1 3402 . . . . . 6
2 sseq1 3212 . . . . . 6
31, 2mpbiri 224 . . . . 5
43eqcoms 2299 . . . 4
543anim3i 1139 . . 3
65ss2abi 3258 . 2
7 df-ps 14322 . 2
8 df-prs 25326 . 2 PresetRel
96, 7, 83sstr4i 3230 1 PresetRel
 Colors of variables: wff set class Syntax hints:   w3a 934   wceq 1632  cab 2282   cin 3164   wss 3165  cuni 3843   cid 4320  ccnv 4704   cres 4707   ccom 4709   wrel 4710  cps 14317  PresetRelcpresetrel 25318 This theorem is referenced by:  posispre  25344 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
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