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Theorem fr0 4561
 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 dffr2 4547 . 2
2 ss0 3658 . . . . 5
32a1d 23 . . . 4
43necon1ad 2671 . . 3
54imp 419 . 2
61, 5mpgbir 1559 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652   wne 2599  wrex 2706  crab 2709   wss 3320  c0 3628   class class class wbr 4212   wfr 4538 This theorem is referenced by:  we0  4577  frsn  4948  frfi  7352  ifr0  27629 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-fr 4541
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