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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 6170 | . 2 recs | |
2 | tfrlem.1 | . . 3 | |
3 | 2 | unieqi 3716 | . 2 |
4 | 1, 3 | eqtr4i 2141 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 cab 2103 wral 2393 wrex 2394 cuni 3706 con0 4255 cres 4511 wfn 5088 cfv 5093 recscrecs 6169 |
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-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-uni 3707 df-recs 6170 |
This theorem is referenced by: tfrlem6 6181 tfrlem7 6182 tfrlem8 6183 tfrlem9 6184 tfrlemibfn 6193 tfrlemiubacc 6195 tfrlemi14d 6198 tfrexlem 6199 |
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