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Theorem po0 4520
 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 3734 . 2
2 df-po 4505 . 2
31, 2mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wral 2707  c0 3630   class class class wbr 4214   wpo 4503 This theorem is referenced by:  so0  4538  posn  4948  dfpo2  25380  ipo0  27630 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-nul 3631  df-po 4505
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