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Mirrors > Home > ILE Home > Th. List > fnoprabg | Unicode version |
Description: Functionality and domain of an operation class abstraction. (Contributed by NM, 28-Aug-2007.) |
Ref | Expression |
---|---|
fnoprabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eumo 2009 | . . . . . 6 | |
2 | 1 | imim2i 12 | . . . . 5 |
3 | moanimv 2052 | . . . . 5 | |
4 | 2, 3 | sylibr 133 | . . . 4 |
5 | 4 | 2alimi 1417 | . . 3 |
6 | funoprabg 5838 | . . 3 | |
7 | 5, 6 | syl 14 | . 2 |
8 | dmoprab 5820 | . . 3 | |
9 | nfa1 1506 | . . . 4 | |
10 | nfa2 1543 | . . . 4 | |
11 | simpl 108 | . . . . . . . 8 | |
12 | 11 | exlimiv 1562 | . . . . . . 7 |
13 | euex 2007 | . . . . . . . . . 10 | |
14 | 13 | imim2i 12 | . . . . . . . . 9 |
15 | 14 | ancld 323 | . . . . . . . 8 |
16 | 19.42v 1862 | . . . . . . . 8 | |
17 | 15, 16 | syl6ibr 161 | . . . . . . 7 |
18 | 12, 17 | impbid2 142 | . . . . . 6 |
19 | 18 | sps 1502 | . . . . 5 |
20 | 19 | sps 1502 | . . . 4 |
21 | 9, 10, 20 | opabbid 3963 | . . 3 |
22 | 8, 21 | syl5eq 2162 | . 2 |
23 | df-fn 5096 | . 2 | |
24 | 7, 22, 23 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 weu 1977 wmo 1978 copab 3958 cdm 4509 wfun 5087 wfn 5088 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-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 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-fun 5095 df-fn 5096 df-oprab 5746 |
This theorem is referenced by: fnoprab 5842 ovg 5877 |
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