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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 5420 | . . . . . 6 | |
2 | 1 | iuneq2d 3838 | . . . . 5 |
3 | 2 | uneq2d 3230 | . . . 4 |
4 | 3 | mpteq2dv 4019 | . . 3 |
5 | recseq 6203 | . . 3 recs recs | |
6 | 4, 5 | syl 14 | . 2 recs recs |
7 | df-irdg 6267 | . 2 recs | |
8 | df-irdg 6267 | . 2 recs | |
9 | 6, 7, 8 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cvv 2686 cun 3069 ciun 3813 cmpt 3989 cdm 4539 cfv 5123 recscrecs 6201 crdg 6266 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-iota 5088 df-fv 5131 df-recs 6202 df-irdg 6267 |
This theorem is referenced by: omv 6351 oeiv 6352 |
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