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Mirrors > Home > ILE Home > Th. List > rdgfun | Unicode version |
Description: The recursive definition generator is a function. (Contributed by Mario Carneiro, 16-Nov-2014.) |
Ref | Expression |
---|---|
rdgfun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2137 | . . 3 | |
2 | 1 | tfrlem7 6207 | . 2 recs |
3 | df-irdg 6260 | . . 3 recs | |
4 | 3 | funeqi 5139 | . 2 recs |
5 | 2, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 cab 2123 wral 2414 wrex 2415 cvv 2681 cun 3064 ciun 3808 cmpt 3984 con0 4280 cdm 4534 cres 4536 wfun 5112 wfn 5113 cfv 5118 recscrecs 6194 crdg 6259 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-setind 4447 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-iun 3810 df-br 3925 df-opab 3985 df-mpt 3986 df-tr 4022 df-id 4210 df-iord 4283 df-on 4285 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 df-irdg 6260 |
This theorem is referenced by: rdgivallem 6271 |
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