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Mirrors > Home > ILE Home > Th. List > fnovex | Unicode version |
Description: The result of an operation is a set. (Contributed by Jim Kingdon, 15-Jan-2019.) |
Ref | Expression |
---|---|
fnovex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5777 | . 2 | |
2 | opelxp 4569 | . . . 4 | |
3 | funfvex 5438 | . . . . 5 | |
4 | 3 | funfni 5223 | . . . 4 |
5 | 2, 4 | sylan2br 286 | . . 3 |
6 | 5 | 3impb 1177 | . 2 |
7 | 1, 6 | eqeltrid 2226 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wcel 1480 cvv 2686 cop 3530 cxp 4537 wfn 5118 cfv 5123 (class class class)co 5774 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fn 5126 df-fv 5131 df-ov 5777 |
This theorem is referenced by: ovelrn 5919 mapsnen 6705 map1 6706 mapen 6740 mapdom1g 6741 mapxpen 6742 xpmapenlem 6743 fzen 9823 hashfacen 10579 topnfn 12125 topnvalg 12132 restbasg 12337 tgrest 12338 restco 12343 lmfval 12361 cnfval 12363 cnpfval 12364 cnpval 12367 txrest 12445 ismet 12513 isxmet 12514 xmetunirn 12527 |
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