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Theorem tfrlem3a 7050
 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.)
Hypotheses
Ref Expression
tfrlem3.1
tfrlem3.2
Assertion
Ref Expression
tfrlem3a
Distinct variable groups:   ,,,,,   ,,,,,
Allowed substitution hints:   (,,,,)

Proof of Theorem tfrlem3a
StepHypRef Expression
1 tfrlem3.2 . 2
2 fneq12 5630 . . . 4
3 simpll 758 . . . . . . 7
4 simpr 462 . . . . . . 7
53, 4fveq12d 5831 . . . . . 6
63, 4reseq12d 5068 . . . . . . 7
76fveq2d 5829 . . . . . 6
85, 7eqeq12d 2443 . . . . 5
9 simplr 760 . . . . 5
108, 9cbvraldva2 3000 . . . 4
112, 10anbi12d 715 . . 3
1211cbvrexdva 3003 . 2
13 tfrlem3.1 . 2
141, 12, 13elab2 3163 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wceq 1437   wcel 1872  cab 2414  wral 2714  wrex 2715  cvv 3022   cres 4798  con0 5385   wfn 5539  cfv 5544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rex 2720  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386  df-ss 3393  df-nul 3705  df-if 3855  df-sn 3942  df-pr 3944  df-op 3948  df-uni 4163  df-br 4367  df-opab 4426  df-xp 4802  df-rel 4803  df-cnv 4804  df-co 4805  df-dm 4806  df-res 4808  df-iota 5508  df-fun 5546  df-fn 5547  df-fv 5552 This theorem is referenced by:  tfrlem3  7051  tfrlem5  7053  tfrlem9a  7059
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