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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 5856 | . 2 | |
2 | opelxp 4641 | . . . 4 | |
3 | funfvex 5513 | . . . . 5 | |
4 | 3 | funfni 5298 | . . . 4 |
5 | 2, 4 | sylan2br 286 | . . 3 |
6 | 5 | 3impb 1194 | . 2 |
7 | 1, 6 | eqeltrid 2257 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 973 wcel 2141 cvv 2730 cop 3586 cxp 4609 wfn 5193 cfv 5198 (class class class)co 5853 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fn 5201 df-fv 5206 df-ov 5856 |
This theorem is referenced by: ovelrn 6001 mapsnen 6789 map1 6790 mapen 6824 mapdom1g 6825 mapxpen 6826 xpmapenlem 6827 fzen 9999 hashfacen 10771 omctfn 12398 topnfn 12584 topnvalg 12591 ismhm 12685 restbasg 12962 tgrest 12963 restco 12968 lmfval 12986 cnfval 12988 cnpfval 12989 cnpval 12992 txrest 13070 ismet 13138 isxmet 13139 xmetunirn 13152 |
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