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Mirrors > Home > ILE Home > Th. List > tfr2a | Unicode version |
Description: A weak version of transfinite recursion. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
tfr.1 | recs |
Ref | Expression |
---|---|
tfr2a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2117 | . . . 4 | |
2 | 1 | tfrlem9 6184 | . . 3 recs recs recs |
3 | tfr.1 | . . . 4 recs | |
4 | 3 | dmeqi 4710 | . . 3 recs |
5 | 2, 4 | eleq2s 2212 | . 2 recs recs |
6 | 3 | fveq1i 5390 | . 2 recs |
7 | 3 | reseq1i 4785 | . . 3 recs |
8 | 7 | fveq2i 5392 | . 2 recs |
9 | 5, 6, 8 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cab 2103 wral 2393 wrex 2394 con0 4255 cdm 4509 cres 4511 wfn 5088 cfv 5093 recscrecs 6169 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-setind 4422 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-tr 3997 df-id 4185 df-iord 4258 df-on 4260 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-res 4521 df-iota 5058 df-fun 5095 df-fn 5096 df-fv 5101 df-recs 6170 |
This theorem is referenced by: tfr0 6188 tfri2d 6201 tfrcl 6229 tfri2 6231 frecsuclem 6271 |
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