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Theorem we0 4817
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 4801 . 2  |-  R  Fr  (/)
2 so0 4776 . 2  |-  R  Or  (/)
3 df-we 4783 . 2  |-  ( R  We  (/)  <->  ( R  Fr  (/) 
/\  R  Or  (/) ) )
41, 2, 3mpbir2an 921 1  |-  R  We  (/)
Colors of variables: wff setvar class
Syntax hints:   (/)c0 3737    Or wor 4742    Fr wfr 4778    We wwe 4780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-in 3420  df-ss 3427  df-nul 3738  df-po 4743  df-so 4744  df-fr 4781  df-we 4783
This theorem is referenced by:  ord0  4873  cantnf0  8046  cantnf  8064  cantnfOLD  8086  wemapwe  8091  wemapweOLD  8092  ltweuz  12026
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