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Theorem dffr3 5236
 Description: Alternate definition of well-founded relation. Definition 6.21 of [TakeutiZaring] p. 30. (Contributed by NM, 23-Apr-2004.) (Revised by Mario Carneiro, 23-Jun-2015.)
Assertion
Ref Expression
dffr3
Distinct variable groups:   ,,   ,,

Proof of Theorem dffr3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffr2 4547 . 2
2 vex 2959 . . . . . . . . 9
3 iniseg 5235 . . . . . . . . 9
42, 3ax-mp 8 . . . . . . . 8
54ineq2i 3539 . . . . . . 7
6 dfrab3 3617 . . . . . . 7
75, 6eqtr4i 2459 . . . . . 6
87eqeq1i 2443 . . . . 5
98rexbii 2730 . . . 4
109imbi2i 304 . . 3
1110albii 1575 . 2
121, 11bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  cab 2422   wne 2599  wrex 2706  crab 2709  cvv 2956   cin 3319   wss 3320  c0 3628  csn 3814   class class class wbr 4212   wfr 4538  ccnv 4877  cima 4881 This theorem is referenced by:  isofrlem  6060  dffr4  25457 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  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-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-fr 4541  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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