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Mirrors > Home > ILE Home > Th. List > recseq | Unicode version |
Description: Equality theorem for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.) |
Ref | Expression |
---|---|
recseq | recs recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1 5495 | . . . . . . . 8 | |
2 | 1 | eqeq2d 2182 | . . . . . . 7 |
3 | 2 | ralbidv 2470 | . . . . . 6 |
4 | 3 | anbi2d 461 | . . . . 5 |
5 | 4 | rexbidv 2471 | . . . 4 |
6 | 5 | abbidv 2288 | . . 3 |
7 | 6 | unieqd 3807 | . 2 |
8 | df-recs 6284 | . 2 recs | |
9 | df-recs 6284 | . 2 recs | |
10 | 7, 8, 9 | 3eqtr4g 2228 | 1 recs recs |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 cab 2156 wral 2448 wrex 2449 cuni 3796 con0 4348 cres 4613 wfn 5193 cfv 5198 recscrecs 6283 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-uni 3797 df-br 3990 df-iota 5160 df-fv 5206 df-recs 6284 |
This theorem is referenced by: rdgeq1 6350 rdgeq2 6351 freceq1 6371 freceq2 6372 frecsuclem 6385 |
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