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Mirrors > Home > ILE Home > Th. List > frecex | Unicode version |
Description: Finite recursion produces a set. (Contributed by Jim Kingdon, 20-Aug-2021.) |
Ref | Expression |
---|---|
frecex | frec |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-frec 6341 | . 2 frec recs | |
2 | tfrfun 6270 | . . 3 recs | |
3 | omex 4555 | . . 3 | |
4 | resfunexg 5691 | . . 3 recs recs | |
5 | 2, 3, 4 | mp2an 423 | . 2 recs |
6 | 1, 5 | eqeltri 2230 | 1 frec |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 698 wceq 1335 wcel 2128 cab 2143 wrex 2436 cvv 2712 c0 3395 cmpt 4028 csuc 4328 com 4552 cdm 4589 cres 4591 wfun 5167 cfv 5173 recscrecs 6254 freccfrec 6340 |
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-coll 4082 ax-sep 4085 ax-pow 4138 ax-pr 4172 ax-setind 4499 ax-iinf 4550 |
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-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-int 3810 df-iun 3853 df-br 3968 df-opab 4029 df-mpt 4030 df-tr 4066 df-id 4256 df-iord 4329 df-on 4331 df-iom 4553 df-xp 4595 df-rel 4596 df-cnv 4597 df-co 4598 df-dm 4599 df-rn 4600 df-res 4601 df-ima 4602 df-iota 5138 df-fun 5175 df-fn 5176 df-f 5177 df-f1 5178 df-fo 5179 df-f1o 5180 df-fv 5181 df-recs 6255 df-frec 6341 |
This theorem is referenced by: seqex 10356 ctinfom 12253 |
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