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Mirrors > Home > ILE Home > Th. List > tfrlem3 | Unicode version |
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.) |
Ref | Expression |
---|---|
tfrlem3.1 |
Ref | Expression |
---|---|
tfrlem3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlem3.1 | . . 3 | |
2 | vex 2715 | . . 3 | |
3 | 1, 2 | tfrlem3a 6257 | . 2 |
4 | 3 | abbi2i 2272 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 cab 2143 wral 2435 wrex 2436 con0 4323 cres 4588 wfn 5165 cfv 5170 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-res 4598 df-iota 5135 df-fun 5172 df-fn 5173 df-fv 5178 |
This theorem is referenced by: tfrlem4 6260 tfrlem8 6265 tfrlemi1 6279 tfrexlem 6281 tfri1d 6282 tfrex 6315 |
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