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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 |
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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 5522 |
. 2
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3 | 1, 2 | ax-mp 7 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-coll 3954 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-csb 2934 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-iun 3732 df-br 3846 df-opab 3900 df-mpt 3901 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-iota 4980 df-fun 5017 df-fn 5018 df-f 5019 df-f1 5020 df-fo 5021 df-f1o 5022 df-fv 5023 |
This theorem is referenced by: eufnfv 5525 abrexex 5888 ofmres 5907 frec2uzrand 9808 frec2uzf1od 9809 frecfzennn 9829 0tonninf 9841 1tonninf 9842 hashinfom 10182 absval 10430 climle 10718 climcvg1nlem 10734 iserabs 10865 isumshft 10880 divcnv 10887 trireciplem 10890 expcnvap0 10892 expcnvre 10893 expcnv 10894 explecnv 10895 geolim 10901 geo2lim 10906 mertenslem2 10926 eftlub 10976 peano4nninf 11851 peano3nninf 11852 nninfsellemeq 11861 nninfsellemeqinf 11863 |
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