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Theorem we0 4098
 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
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fr0 4088 . 2
2 ral0 3322 . 2
3 df-wetr 4071 . 2
41, 2, 3mpbir2an 849 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wral 2306  c0 3224   class class class wbr 3764   wfr 4065   wwe 4067 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-nul 3225  df-frfor 4068  df-frind 4069  df-wetr 4071 This theorem is referenced by: (None)
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