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Mirrors > Home > ILE Home > Th. List > ov | Unicode version |
Description: The value of an operation class abstraction. (Contributed by NM, 16-May-1995.) (Revised by David Abernethy, 19-Jun-2012.) |
Ref | Expression |
---|---|
ov.1 | |
ov.2 | |
ov.3 | |
ov.4 | |
ov.5 | |
ov.6 |
Ref | Expression |
---|---|
ov |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5856 | . . . . 5 | |
2 | ov.6 | . . . . . 6 | |
3 | 2 | fveq1i 5497 | . . . . 5 |
4 | 1, 3 | eqtri 2191 | . . . 4 |
5 | 4 | eqeq1i 2178 | . . 3 |
6 | ov.5 | . . . . . 6 | |
7 | 6 | fnoprab 5956 | . . . . 5 |
8 | eleq1 2233 | . . . . . . . 8 | |
9 | 8 | anbi1d 462 | . . . . . . 7 |
10 | eleq1 2233 | . . . . . . . 8 | |
11 | 10 | anbi2d 461 | . . . . . . 7 |
12 | 9, 11 | opelopabg 4253 | . . . . . 6 |
13 | 12 | ibir 176 | . . . . 5 |
14 | fnopfvb 5538 | . . . . 5 | |
15 | 7, 13, 14 | sylancr 412 | . . . 4 |
16 | ov.1 | . . . . 5 | |
17 | ov.2 | . . . . . . 7 | |
18 | 9, 17 | anbi12d 470 | . . . . . 6 |
19 | ov.3 | . . . . . . 7 | |
20 | 11, 19 | anbi12d 470 | . . . . . 6 |
21 | ov.4 | . . . . . . 7 | |
22 | 21 | anbi2d 461 | . . . . . 6 |
23 | 18, 20, 22 | eloprabg 5941 | . . . . 5 |
24 | 16, 23 | mp3an3 1321 | . . . 4 |
25 | 15, 24 | bitrd 187 | . . 3 |
26 | 5, 25 | syl5bb 191 | . 2 |
27 | 26 | bianabs 606 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 weu 2019 wcel 2141 cvv 2730 cop 3586 copab 4049 wfn 5193 cfv 5198 (class class class)co 5853 coprab 5854 |
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-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fn 5201 df-fv 5206 df-ov 5856 df-oprab 5857 |
This theorem is referenced by: (None) |
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