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Mirrors > Home > ILE Home > Th. List > rdgeq2 | 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 |
---|---|
rdgeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1 3254 | . . . 4 | |
2 | 1 | mpteq2dv 4055 | . . 3 |
3 | recseq 6253 | . . 3 recs recs | |
4 | 2, 3 | syl 14 | . 2 recs recs |
5 | df-irdg 6317 | . 2 recs | |
6 | df-irdg 6317 | . 2 recs | |
7 | 4, 5, 6 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 cvv 2712 cun 3100 ciun 3849 cmpt 4025 cdm 4586 cfv 5170 recscrecs 6251 crdg 6316 |
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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-uni 3773 df-br 3966 df-opab 4026 df-mpt 4027 df-iota 5135 df-fv 5178 df-recs 6252 df-irdg 6317 |
This theorem is referenced by: rdg0g 6335 oav 6401 |
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