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Mirrors > Home > ILE Home > Th. List > rdgeq1 | Unicode version |
Description: Equality theorem for the recursive definition generator. (Contributed by NM, 9-Apr-1995.) (Revised by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
rdgeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1 5177 | . . . . . 6 | |
2 | 1 | iuneq2d 3682 | . . . . 5 |
3 | 2 | uneq2d 3097 | . . . 4 |
4 | 3 | mpteq2dv 3848 | . . 3 |
5 | recseq 5921 | . . 3 recs recs | |
6 | 4, 5 | syl 14 | . 2 recs recs |
7 | df-irdg 5957 | . 2 recs | |
8 | df-irdg 5957 | . 2 recs | |
9 | 6, 7, 8 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 cvv 2557 cun 2915 ciun 3657 cmpt 3818 cdm 4345 cfv 4902 recscrecs 5919 crdg 5956 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-uni 3581 df-iun 3659 df-br 3765 df-opab 3819 df-mpt 3820 df-iota 4867 df-fv 4910 df-recs 5920 df-irdg 5957 |
This theorem is referenced by: omv 6035 oeiv 6036 |
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