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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 5197 | . . . . . . . 8 | |
2 | 1 | eqeq2d 2092 | . . . . . . 7 |
3 | 2 | ralbidv 2368 | . . . . . 6 |
4 | 3 | anbi2d 451 | . . . . 5 |
5 | 4 | rexbidv 2369 | . . . 4 |
6 | 5 | abbidv 2196 | . . 3 |
7 | 6 | unieqd 3612 | . 2 |
8 | df-recs 5943 | . 2 recs | |
9 | df-recs 5943 | . 2 recs | |
10 | 7, 8, 9 | 3eqtr4g 2138 | 1 recs recs |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 cab 2067 wral 2348 wrex 2349 cuni 3601 con0 4118 cres 4365 wfn 4917 cfv 4922 recscrecs 5942 |
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-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-recs 5943 |
This theorem is referenced by: rdgeq1 5981 rdgeq2 5982 freceq1 6002 freceq2 6003 frecsuclem1 6010 frecsuclem2 6012 |
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