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Theorem tfrlem3 5926
 Description: Lemma for transfinite recursion. Let be the class of "acceptable" functions. The final thing we're interested in is the union of all these acceptable functions. This lemma just changes some bound variables in for later use. (Contributed by NM, 9-Apr-1995.)
Hypothesis
Ref Expression
tfrlem3.1
Assertion
Ref Expression
tfrlem3
Distinct variable groups:   ,   ,,,,,,
Allowed substitution hints:   (,,,,)

Proof of Theorem tfrlem3
StepHypRef Expression
1 tfrlem3.1 . . 3
2 vex 2560 . . 3
31, 2tfrlem3a 5925 . 2
43abbi2i 2152 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  cab 2026  wral 2306  wrex 2307  con0 4100   cres 4347   wfn 4897  cfv 4902 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-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 This theorem is referenced by:  tfrlem4  5929  tfrlem8  5934  tfrlemi1  5946  tfrexlem  5948  tfri1d  5949  tfrex  5954
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