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Theorem fri 4536
 Description: Property of well-founded relation (one direction of definition). (Contributed by NM, 18-Mar-1997.)
Assertion
Ref Expression
fri
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem fri
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-fr 4533 . . 3
2 sseq1 3361 . . . . . 6
3 neeq1 2606 . . . . . 6
42, 3anbi12d 692 . . . . 5
5 raleq 2896 . . . . . 6
65rexeqbi1dv 2905 . . . . 5
74, 6imbi12d 312 . . . 4
87spcgv 3028 . . 3
91, 8syl5bi 209 . 2
109imp31 422 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698   wss 3312  c0 3620   class class class wbr 4204   wfr 4530 This theorem is referenced by:  frc  4540  fr2nr  4552  frminex  4554  wereu  4570  wereu2  4571  fr3nr  4752  frfi  7344  fimax2g  7345  wofib  7506  wemapso  7512  wemapso2  7513  noinfep  7606  noinfepOLD  7607  cflim2  8135  isfin1-3  8258  fin12  8285  fpwwe2lem12  8508  fpwwe2lem13  8509  fpwwe2  8510  frinfm  26428  fdc  26440  fnwe2lem2  27117  bnj110  29166 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-fr 4533
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