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Theorem tfrlem6 5932
 Description: Lemma for transfinite recursion. The union of all acceptable functions is a relation. (Contributed by NM, 8-Aug-1994.) (Revised by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
tfrlem.1
Assertion
Ref Expression
tfrlem6 recs
Distinct variable group:   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem tfrlem6
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reluni 4460 . . 3
2 tfrlem.1 . . . . 5
32tfrlem4 5929 . . . 4
4 funrel 4919 . . . 4
53, 4syl 14 . . 3
61, 5mprgbir 2379 . 2
72recsfval 5931 . . 3 recs
87releqi 4423 . 2 recs
96, 8mpbir 134 1 recs
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wcel 1393  cab 2026  wral 2306  wrex 2307  cuni 3580  con0 4100   cres 4347   wrel 4350   wfun 4896   wfn 4897  cfv 4902  recscrecs 5919 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-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-3an 887  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-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-iun 3659  df-br 3765  df-opab 3819  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-res 4357  df-iota 4867  df-fun 4904  df-fn 4905  df-fv 4910  df-recs 5920 This theorem is referenced by:  tfrlem7  5933
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