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Theorem so0 4054
Description: Any relation is a strict ordering of the empty set. (Contributed by NM, 16-Mar-1997.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
so0  R  Or  (/)

Proof of Theorem so0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 po0 4039 . 2  R  Po  (/)
2 ral0 3316 . 2  (/)  (/)  (/)  R  R  R
3 df-iso 4025 . 2  R  Or  (/)  R  Po  (/)  (/)  (/)  (/)  R  R  R
41, 2, 3mpbir2an 848 1  R  Or  (/)
Colors of variables: wff set class
Syntax hints:   wi 4   wo 628  wral 2300   (/)c0 3218   class class class wbr 3755    Po wpo 4022    Or wor 4023
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-dif 2914  df-nul 3219  df-po 4024  df-iso 4025
This theorem is referenced by: (None)
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