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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 4853 |
. 2
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2 | funfveu 5131 |
. . 3
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3 | euiotaex 4826 |
. . 3
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4 | 2, 3 | syl 14 |
. 2
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5 | 1, 4 | syl5eqel 2121 |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-sbc 2759 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-opab 3810 df-id 4021 df-cnv 4296 df-co 4297 df-dm 4298 df-iota 4810 df-fun 4847 df-fv 4853 |
This theorem is referenced by: fnbrfvb 5157 fvelrnb 5164 funimass4 5167 fvelimab 5172 fniinfv 5174 funfvdm 5179 dmfco 5184 fvco2 5185 eqfnfv 5208 fndmdif 5215 fndmin 5217 fvimacnvi 5224 fvimacnv 5225 funconstss 5228 fniniseg 5230 fniniseg2 5232 fnniniseg2 5233 rexsupp 5234 fvelrn 5241 rexrn 5247 ralrn 5248 dff3im 5255 fmptco 5273 fsn2 5280 fnressn 5292 resfunexg 5325 eufnfv 5332 funfvima3 5335 rexima 5337 ralima 5338 fniunfv 5344 elunirn 5348 dff13 5350 foeqcnvco 5373 f1eqcocnv 5374 isocnv2 5395 isoini 5400 f1oiso 5408 fnovex 5481 suppssof1 5670 offveqb 5672 1stexg 5736 2ndexg 5737 smoiso 5858 rdgtfr 5901 rdgruledefgg 5902 rdgivallem 5908 frectfr 5924 frecrdg 5931 freccl 5932 en1 6215 fundmen 6222 |
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