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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 2689 | . . 3 | |
3 | 1, 2 | tfrlem3a 6207 | . 2 |
4 | 3 | abbi2i 2254 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 cab 2125 wral 2416 wrex 2417 con0 4285 cres 4541 wfn 5118 cfv 5123 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-res 4551 df-iota 5088 df-fun 5125 df-fn 5126 df-fv 5131 |
This theorem is referenced by: tfrlem4 6210 tfrlem8 6215 tfrlemi1 6229 tfrexlem 6231 tfri1d 6232 tfrex 6265 |
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