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Theorem tfrlem3a 6631
 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, 22-Jul-2012.)
Hypothesis
Ref Expression
tfrlem3a.1
Assertion
Ref Expression
tfrlem3a
Distinct variable groups:   ,,,   ,,
Allowed substitution hints:   (,,,)   (,)

Proof of Theorem tfrlem3a
StepHypRef Expression
1 tfrlem3a.1 . 2
2 fneq1 5526 . . . . 5
3 fveq1 5719 . . . . . . 7
4 reseq1 5132 . . . . . . . 8
54fveq2d 5724 . . . . . . 7
63, 5eqeq12d 2449 . . . . . 6
76ralbidv 2717 . . . . 5
82, 7anbi12d 692 . . . 4
98rexbidv 2718 . . 3
109cbvabv 2554 . 2
111, 10eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652  cab 2421  wral 2697  wrex 2698  con0 4573   cres 4872   wfn 5441  cfv 5446 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-3an 938  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-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-res 4882  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454
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