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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 2157 | . . 3 | |
2 | 1 | tfrlem7 6265 | . 2 recs |
3 | df-irdg 6318 | . . 3 recs | |
4 | 3 | funeqi 5192 | . 2 recs |
5 | 2, 4 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 cab 2143 wral 2435 wrex 2436 cvv 2712 cun 3100 ciun 3850 cmpt 4026 con0 4324 cdm 4587 cres 4589 wfun 5165 wfn 5166 cfv 5171 recscrecs 6252 crdg 6317 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-setind 4497 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-iun 3852 df-br 3967 df-opab 4027 df-mpt 4028 df-tr 4064 df-id 4254 df-iord 4327 df-on 4329 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-res 4599 df-iota 5136 df-fun 5173 df-fn 5174 df-fv 5179 df-recs 6253 df-irdg 6318 |
This theorem is referenced by: rdgivallem 6329 |
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