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Mirrors > Home > ILE Home > Th. List > mptex | Unicode version |
Description: If the domain of a function given by maps-to notation is a set, the function is a set. (Contributed by NM, 22-Apr-2005.) (Revised by Mario Carneiro, 20-Dec-2013.) |
Ref | Expression |
---|---|
mptex.1 |
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Ref | Expression |
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mptex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptex.1 |
. 2
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2 | mptexg 5742 |
. 2
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3 | 1, 2 | ax-mp 5 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-coll 4119 ax-sep 4122 ax-pow 4175 ax-pr 4210 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2740 df-sbc 2964 df-csb 3059 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-iun 3889 df-br 4005 df-opab 4066 df-mpt 4067 df-id 4294 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-ima 4640 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-f1 5222 df-fo 5223 df-f1o 5224 df-fv 5225 |
This theorem is referenced by: mptrabex 5745 eufnfv 5748 abrexex 6118 ofmres 6137 difinfsn 7099 ctmlemr 7107 ctssdclemn0 7109 ctssdc 7112 enumct 7114 frec2uzrand 10405 frec2uzf1od 10406 frecfzennn 10426 uzennn 10436 0tonninf 10439 1tonninf 10440 hashinfom 10758 absval 11010 climle 11342 climcvg1nlem 11357 iserabs 11483 isumshft 11498 divcnv 11505 trireciplem 11508 expcnvap0 11510 expcnvre 11511 expcnv 11512 explecnv 11513 geolim 11519 geo2lim 11524 mertenslem2 11544 eftlub 11698 1arithlem1 12361 1arith 12365 ctiunct 12441 restfn 12692 peano4nninf 14758 peano3nninf 14759 nninfsellemeq 14766 nninfsellemeqinf 14768 dceqnconst 14810 dcapnconst 14811 |
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