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Theorem so0 4807
 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

Proof of Theorem so0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 po0 4789 . 2
2 ral0 3904 . 2
3 df-so 4775 . 2
41, 2, 3mpbir2an 928 1
 Colors of variables: wff setvar class Syntax hints:   w3o 981  wral 2771  c0 3761   class class class wbr 4423   wpo 4772   wor 4773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-v 3082  df-dif 3439  df-nul 3762  df-po 4774  df-so 4775 This theorem is referenced by:  we0  4848  wemapso2  8077
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