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Theorem we0 4826
Description: Any relation is a well-ordering of the empty set. (Contributed by NM, 16-Mar-1997.)
Assertion
Ref Expression
we0  |-  R  We  (/)

Proof of Theorem we0
StepHypRef Expression
1 fr0 4810 . 2  |-  R  Fr  (/)
2 so0 4785 . 2  |-  R  Or  (/)
3 df-we 4792 . 2  |-  ( R  We  (/)  <->  ( R  Fr  (/) 
/\  R  Or  (/) ) )
41, 2, 3mpbir2an 911 1  |-  R  We  (/)
Colors of variables: wff setvar class
Syntax hints:   (/)c0 3748    Or wor 4751    Fr wfr 4787    We wwe 4789
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-in 3446  df-ss 3453  df-nul 3749  df-po 4752  df-so 4753  df-fr 4790  df-we 4792
This theorem is referenced by:  ord0  4882  cantnf0  7998  cantnf  8016  cantnfOLD  8038  wemapwe  8043  wemapweOLD  8044  ltweuz  11905
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