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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 2164 | . . . 4 | |
2 | 1 | tfrlem9 6279 | . . 3 recs recs recs |
3 | tfr.1 | . . . 4 recs | |
4 | 3 | dmeqi 4800 | . . 3 recs |
5 | 2, 4 | eleq2s 2259 | . 2 recs recs |
6 | 3 | fveq1i 5482 | . 2 recs |
7 | 3 | reseq1i 4875 | . . 3 recs |
8 | 7 | fveq2i 5484 | . 2 recs |
9 | 5, 6, 8 | 3eqtr4g 2222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 cab 2150 wral 2442 wrex 2443 con0 4336 cdm 4599 cres 4601 wfn 5178 cfv 5183 recscrecs 6264 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 ax-setind 4509 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-sbc 2948 df-csb 3042 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-iun 3863 df-br 3978 df-opab 4039 df-mpt 4040 df-tr 4076 df-id 4266 df-iord 4339 df-on 4341 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-res 4611 df-iota 5148 df-fun 5185 df-fn 5186 df-fv 5191 df-recs 6265 |
This theorem is referenced by: tfr0 6283 tfri2d 6296 tfrcl 6324 tfri2 6326 frecsuclem 6366 |
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