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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 6264 | . 2 recs | |
2 | tfrlem.1 | . . 3 | |
3 | 2 | unieqi 3793 | . 2 |
4 | 1, 3 | eqtr4i 2188 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 cab 2150 wral 2442 wrex 2443 cuni 3783 con0 4335 cres 4600 wfn 5177 cfv 5182 recscrecs 6263 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-uni 3784 df-recs 6264 |
This theorem is referenced by: tfrlem6 6275 tfrlem7 6276 tfrlem8 6277 tfrlem9 6278 tfrlemibfn 6287 tfrlemiubacc 6289 tfrlemi14d 6292 tfrexlem 6293 |
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