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Mirrors > Home > ILE Home > Th. List > resoprab | Unicode version |
Description: Restriction of an operation class abstraction. (Contributed by NM, 10-Feb-2007.) |
Ref | Expression |
---|---|
resoprab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resopab 4672 | . . 3 | |
2 | 19.42vv 1829 | . . . . 5 | |
3 | an12 525 | . . . . . . 7 | |
4 | eleq1 2141 | . . . . . . . . . 10 | |
5 | opelxp 4392 | . . . . . . . . . 10 | |
6 | 4, 5 | syl6bb 194 | . . . . . . . . 9 |
7 | 6 | anbi1d 452 | . . . . . . . 8 |
8 | 7 | pm5.32i 441 | . . . . . . 7 |
9 | 3, 8 | bitri 182 | . . . . . 6 |
10 | 9 | 2exbii 1537 | . . . . 5 |
11 | 2, 10 | bitr3i 184 | . . . 4 |
12 | 11 | opabbii 3845 | . . 3 |
13 | 1, 12 | eqtri 2101 | . 2 |
14 | dfoprab2 5572 | . . 3 | |
15 | 14 | reseq1i 4626 | . 2 |
16 | dfoprab2 5572 | . 2 | |
17 | 13, 15, 16 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wex 1421 wcel 1433 cop 3401 copab 3838 cxp 4361 cres 4365 coprab 5533 |
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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 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-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 df-xp 4369 df-rel 4370 df-res 4375 df-oprab 5536 |
This theorem is referenced by: resoprab2 5618 |
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