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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 2760 |
. . 3
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2 | 1 | ralimi 2550 |
. 2
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3 | mptfng.1 |
. . 3
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4 | 3 | mptfng 5353 |
. 2
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5 | 2, 4 | sylib 122 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-mpt 4078 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-fun 5230 df-fn 5231 |
This theorem is referenced by: mpt0 5355 fnmptfvd 5633 ralrnmpt 5671 rexrnmpt 5672 fmpt 5679 fmpt2d 5691 f1ocnvd 6086 offval2 6111 ofrfval2 6112 caofinvl 6118 f1od2 6249 frectfr 6414 omfnex 6463 oeiv 6470 mptelixpg 6747 fifo 6992 nnnninfeq 7139 nninfwlporlemd 7183 cc2lem 7278 efcvgfsum 11688 quslem 12762 grpinvfng 12940 neif 13912 tgrest 13940 dvrecap 14448 fnmptd 14827 |
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