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Theorem po0 4769
 Description: Any relation is a partial ordering of the empty set. (Contributed by NM, 28-Mar-1997.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
po0

Proof of Theorem po0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ral0 3873 . 2
2 df-po 4754 . 2
31, 2mpbir 213 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 371  wral 2736  c0 3730   class class class wbr 4401   wpo 4752 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-v 3046  df-dif 3406  df-nul 3731  df-po 4754 This theorem is referenced by:  so0  4787  posn  4902  dfpo2  30388  ipo0  36796
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