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Mirrors > Home > ILE Home > Th. List > tfrlem6 | Unicode version |
Description: Lemma for transfinite recursion. The union of all acceptable functions is a relation. (Contributed by NM, 8-Aug-1994.) (Revised by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
tfrlem.1 |
Ref | Expression |
---|---|
tfrlem6 | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reluni 4657 | . . 3 | |
2 | tfrlem.1 | . . . . 5 | |
3 | 2 | tfrlem4 6203 | . . . 4 |
4 | funrel 5135 | . . . 4 | |
5 | 3, 4 | syl 14 | . . 3 |
6 | 1, 5 | mprgbir 2488 | . 2 |
7 | 2 | recsfval 6205 | . . 3 recs |
8 | 7 | releqi 4617 | . 2 recs |
9 | 6, 8 | mpbir 145 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wcel 1480 cab 2123 wral 2414 wrex 2415 cuni 3731 con0 4280 cres 4536 wrel 4539 wfun 5112 wfn 5113 cfv 5118 recscrecs 6194 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-iun 3810 df-br 3925 df-opab 3985 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-res 4546 df-iota 5083 df-fun 5120 df-fn 5121 df-fv 5126 df-recs 6195 |
This theorem is referenced by: tfrlem7 6207 |
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