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Theorem we0 4879
Description: Any relation is a well-ordering of the empty set. (Contributed by NM, 16-Mar-1997.)
Assertion
Ref Expression
we0

Proof of Theorem we0
StepHypRef Expression
1 fr0 4863 . 2
2 so0 4838 . 2
3 df-we 4845 . 2
41, 2, 3mpbir2an 920 1
Colors of variables: wff setvar class
Syntax hints:   c0 3784  Orwor 4804  Frwfr 4840  Wewwe 4842
This theorem is referenced by:  ord0  4935  cantnf0  8115  cantnf  8133  cantnfOLD  8155  wemapwe  8160  wemapweOLD  8161  ltweuz  12072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-po 4805  df-so 4806  df-fr 4843  df-we 4845
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