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Mirrors > Home > ILE Home > Th. List > recsfval | Unicode version |
Description: Lemma for transfinite recursion. The definition recs is the union of all acceptable functions. (Contributed by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
tfrlem.1 |
Ref | Expression |
---|---|
recsfval | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-recs 6202 | . 2 recs | |
2 | tfrlem.1 | . . 3 | |
3 | 2 | unieqi 3746 | . 2 |
4 | 1, 3 | eqtr4i 2163 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 cab 2125 wral 2416 wrex 2417 cuni 3736 con0 4285 cres 4541 wfn 5118 cfv 5123 recscrecs 6201 |
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-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-uni 3737 df-recs 6202 |
This theorem is referenced by: tfrlem6 6213 tfrlem7 6214 tfrlem8 6215 tfrlem9 6216 tfrlemibfn 6225 tfrlemiubacc 6227 tfrlemi14d 6230 tfrexlem 6231 |
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