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Theorem isps 14626
 Description: The predicate "is a poset" i.e. a transitive, reflexive, antisymmetric relation. (Contributed by NM, 11-May-2008.)
Assertion
Ref Expression
isps

Proof of Theorem isps
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 releq 4951 . . 3
2 coeq1 5022 . . . . 5
3 coeq2 5023 . . . . 5
42, 3eqtrd 2467 . . . 4
5 id 20 . . . 4
64, 5sseq12d 3369 . . 3
7 cnveq 5038 . . . . 5
85, 7ineq12d 3535 . . . 4
9 unieq 4016 . . . . . 6
109unieqd 4018 . . . . 5
1110reseq2d 5138 . . . 4
128, 11eqeq12d 2449 . . 3
131, 6, 123anbi123d 1254 . 2
14 df-ps 14621 . 2
1513, 14elab2g 3076 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1652   wcel 1725   cin 3311   wss 3312  cuni 4007   cid 4485  ccnv 4869   cres 4872   ccom 4874   wrel 4875  cps 14616 This theorem is referenced by:  psrel  14627  psref2  14628  pstr2  14629  cnvps  14636  psss  14638  letsr  14664 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 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-res 4882  df-ps 14621
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