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Theorem tfrlem3 6640
 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 . 2
2 vex 2961 . . . . 5
3 fneq1 5536 . . . . . . 7
4 fveq1 5729 . . . . . . . . 9
5 reseq1 5142 . . . . . . . . . 10
65fveq2d 5734 . . . . . . . . 9
74, 6eqeq12d 2452 . . . . . . . 8
87ralbidv 2727 . . . . . . 7
93, 8anbi12d 693 . . . . . 6
109rexbidv 2728 . . . . 5
112, 10elab 3084 . . . 4
12 fneq2 5537 . . . . . 6
13 raleq 2906 . . . . . 6
1412, 13anbi12d 693 . . . . 5
1514cbvrexv 2935 . . . 4
1611, 15bitri 242 . . 3
1716abbi2i 2549 . 2
181, 17eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653   wcel 1726  cab 2424  wral 2707  wrex 2708  con0 4583   cres 4882   wfn 5451  cfv 5456 This theorem is referenced by:  tfrlem4  6642  tfrlem5  6643  tfrlem8  6647  tfrlem9a  6649  rdglem1  6675 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-res 4892  df-iota 5420  df-fun 5458  df-fn 5459  df-fv 5464
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