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Mirrors > Home > ILE Home > Th. List > ovigg | Unicode version |
Description: The value of an operation class abstraction. Compare ovig 5860. The condition is been removed. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ovigg.1 | |
ovigg.4 | |
ovigg.5 |
Ref | Expression |
---|---|
ovigg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovigg.1 | . . 3 | |
2 | 1 | eloprabga 5826 | . 2 |
3 | df-ov 5745 | . . . 4 | |
4 | ovigg.5 | . . . . 5 | |
5 | 4 | fveq1i 5390 | . . . 4 |
6 | 3, 5 | eqtri 2138 | . . 3 |
7 | ovigg.4 | . . . . 5 | |
8 | 7 | funoprab 5839 | . . . 4 |
9 | funopfv 5429 | . . . 4 | |
10 | 8, 9 | ax-mp 5 | . . 3 |
11 | 6, 10 | syl5eq 2162 | . 2 |
12 | 2, 11 | syl6bir 163 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 947 wceq 1316 wcel 1465 wmo 1978 cop 3500 wfun 5087 cfv 5093 (class class class)co 5742 coprab 5743 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-ov 5745 df-oprab 5746 |
This theorem is referenced by: ovig 5860 |
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