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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 5828 | . 2 | |
2 | opelxp 4617 | . . . 4 | |
3 | funfvex 5486 | . . . . 5 | |
4 | 3 | funfni 5271 | . . . 4 |
5 | 2, 4 | sylan2br 286 | . . 3 |
6 | 5 | 3impb 1181 | . 2 |
7 | 1, 6 | eqeltrid 2244 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wcel 2128 cvv 2712 cop 3563 cxp 4585 wfn 5166 cfv 5171 (class class class)co 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 4083 ax-pow 4136 ax-pr 4170 |
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 3774 df-br 3967 df-opab 4027 df-id 4254 df-xp 4593 df-cnv 4595 df-co 4596 df-dm 4597 df-iota 5136 df-fun 5173 df-fn 5174 df-fv 5179 df-ov 5828 |
This theorem is referenced by: ovelrn 5970 mapsnen 6757 map1 6758 mapen 6792 mapdom1g 6793 mapxpen 6794 xpmapenlem 6795 fzen 9946 hashfacen 10711 omctfn 12214 topnfn 12398 topnvalg 12405 restbasg 12610 tgrest 12611 restco 12616 lmfval 12634 cnfval 12636 cnpfval 12637 cnpval 12640 txrest 12718 ismet 12786 isxmet 12787 xmetunirn 12800 |
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