Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 5827 | . . . . 5 | |
2 | ov.6 | . . . . . 6 | |
3 | 2 | fveq1i 5469 | . . . . 5 |
4 | 1, 3 | eqtri 2178 | . . . 4 |
5 | 4 | eqeq1i 2165 | . . 3 |
6 | ov.5 | . . . . . 6 | |
7 | 6 | fnoprab 5924 | . . . . 5 |
8 | eleq1 2220 | . . . . . . . 8 | |
9 | 8 | anbi1d 461 | . . . . . . 7 |
10 | eleq1 2220 | . . . . . . . 8 | |
11 | 10 | anbi2d 460 | . . . . . . 7 |
12 | 9, 11 | opelopabg 4228 | . . . . . 6 |
13 | 12 | ibir 176 | . . . . 5 |
14 | fnopfvb 5510 | . . . . 5 | |
15 | 7, 13, 14 | sylancr 411 | . . . 4 |
16 | ov.1 | . . . . 5 | |
17 | ov.2 | . . . . . . 7 | |
18 | 9, 17 | anbi12d 465 | . . . . . 6 |
19 | ov.3 | . . . . . . 7 | |
20 | 11, 19 | anbi12d 465 | . . . . . 6 |
21 | ov.4 | . . . . . . 7 | |
22 | 21 | anbi2d 460 | . . . . . 6 |
23 | 18, 20, 22 | eloprabg 5909 | . . . . 5 |
24 | 16, 23 | mp3an3 1308 | . . . 4 |
25 | 15, 24 | bitrd 187 | . . 3 |
26 | 5, 25 | syl5bb 191 | . 2 |
27 | 26 | bianabs 601 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 weu 2006 wcel 2128 cvv 2712 cop 3563 copab 4024 wfn 5165 cfv 5170 (class class class)co 5824 coprab 5825 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-iota 5135 df-fun 5172 df-fn 5173 df-fv 5178 df-ov 5827 df-oprab 5828 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |