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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 2663 | . . 3 | |
3 | 1, 2 | tfrlem3a 6175 | . 2 |
4 | 3 | abbi2i 2232 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 cab 2103 wral 2393 wrex 2394 con0 4255 cres 4511 wfn 5088 cfv 5093 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-res 4521 df-iota 5058 df-fun 5095 df-fn 5096 df-fv 5101 |
This theorem is referenced by: tfrlem4 6178 tfrlem8 6183 tfrlemi1 6197 tfrexlem 6199 tfri1d 6200 tfrex 6233 |
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