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Mirrors > Home > ILE Home > Th. List > fnmpt | Unicode version |
Description: The maps-to notation defines a function with domain. (Contributed by NM, 9-Apr-2013.) |
Ref | Expression |
---|---|
mptfng.1 |
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Ref | Expression |
---|---|
fnmpt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2633 |
. . 3
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2 | 1 | ralimi 2439 |
. 2
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3 | mptfng.1 |
. . 3
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4 | 3 | mptfng 5154 |
. 2
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5 | 2, 4 | sylib 121 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3965 ax-pow 4017 ax-pr 4047 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2624 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-br 3854 df-opab 3908 df-mpt 3909 df-id 4131 df-xp 4460 df-rel 4461 df-cnv 4462 df-co 4463 df-dm 4464 df-fun 5032 df-fn 5033 |
This theorem is referenced by: mpt0 5156 ralrnmpt 5457 rexrnmpt 5458 fmpt 5465 fmpt2d 5476 f1ocnvd 5862 offval2 5886 ofrfval2 5887 caofinvl 5893 f1od2 6016 frectfr 6181 omfnex 6226 oeiv 6233 mptelixpg 6507 efcvgfsum 11020 neif 11904 nninfalllemn 12201 |
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