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Mirrors > Home > ILE Home > Th. List > funfvex | Unicode version |
Description: The value of a function exists. A special case of Corollary 6.13 of [TakeutiZaring] p. 27. (Contributed by Jim Kingdon, 29-Dec-2018.) |
Ref | Expression |
---|---|
funfvex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fv 4910 |
. 2
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2 | funfveu 5188 |
. . 3
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3 | euiotaex 4883 |
. . 3
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4 | 2, 3 | syl 14 |
. 2
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5 | 1, 4 | syl5eqel 2124 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 |
This theorem is referenced by: fnbrfvb 5214 fvelrnb 5221 funimass4 5224 fvelimab 5229 fniinfv 5231 funfvdm 5236 dmfco 5241 fvco2 5242 eqfnfv 5265 fndmdif 5272 fndmin 5274 fvimacnvi 5281 fvimacnv 5282 funconstss 5285 fniniseg 5287 fniniseg2 5289 fnniniseg2 5290 rexsupp 5291 fvelrn 5298 rexrn 5304 ralrn 5305 dff3im 5312 fmptco 5330 fsn2 5337 fnressn 5349 resfunexg 5382 eufnfv 5389 funfvima3 5392 rexima 5394 ralima 5395 fniunfv 5401 elunirn 5405 dff13 5407 foeqcnvco 5430 f1eqcocnv 5431 isocnv2 5452 isoini 5457 f1oiso 5465 fnovex 5538 suppssof1 5728 offveqb 5730 1stexg 5794 2ndexg 5795 smoiso 5917 rdgtfr 5961 rdgruledefgg 5962 rdgivallem 5968 frectfr 5985 frecrdg 5992 freccl 5993 en1 6279 fundmen 6286 ordiso2 6357 climshft2 9827 |
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