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Theorem fr0 4088
 Description: Any relation is well-founded on the empty set. (Contributed by NM, 17-Sep-1993.)
Assertion
Ref Expression
fr0

Proof of Theorem fr0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-frind 4069 . 2 FrFor
2 0ss 3255 . . . 4
32a1i 9 . . 3
4 df-frfor 4068 . . 3 FrFor
53, 4mpbir 134 . 2 FrFor
61, 5mpgbir 1342 1
 Colors of variables: wff set class Syntax hints:   wi 4  wral 2306   wss 2917  c0 3224   class class class wbr 3764  FrFor wfrfor 4064   wfr 4065 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-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-nul 3225  df-frfor 4068  df-frind 4069 This theorem is referenced by:  we0  4098
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