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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 3119 | . . . 4 | |
2 | 1 | mpteq2dv 3869 | . . 3 |
3 | recseq 5944 | . . 3 recs recs | |
4 | 2, 3 | syl 14 | . 2 recs recs |
5 | df-irdg 5980 | . 2 recs | |
6 | df-irdg 5980 | . 2 recs | |
7 | 4, 5, 6 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 cvv 2601 cun 2971 ciun 3678 cmpt 3839 cdm 4363 cfv 4922 recscrecs 5942 crdg 5979 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-iota 4887 df-fv 4930 df-recs 5943 df-irdg 5980 |
This theorem is referenced by: rdg0g 5998 oav 6057 |
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