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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 5177 | . . . . . . . 8 | |
2 | 1 | eqeq2d 2051 | . . . . . . 7 |
3 | 2 | ralbidv 2326 | . . . . . 6 |
4 | 3 | anbi2d 437 | . . . . 5 |
5 | 4 | rexbidv 2327 | . . . 4 |
6 | 5 | abbidv 2155 | . . 3 |
7 | 6 | unieqd 3591 | . 2 |
8 | df-recs 5920 | . 2 recs | |
9 | df-recs 5920 | . 2 recs | |
10 | 7, 8, 9 | 3eqtr4g 2097 | 1 recs recs |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 cab 2026 wral 2306 wrex 2307 cuni 3580 con0 4100 cres 4347 wfn 4897 cfv 4902 recscrecs 5919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-recs 5920 |
This theorem is referenced by: rdgeq1 5958 rdgeq2 5959 freceq1 5979 freceq2 5980 frecsuclem1 5987 frecsuclem2 5989 |
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