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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 |
Ref | Expression |
---|---|
mptex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptex.1 | . 2 | |
2 | mptexg 5613 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 cmpt 3959 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-coll 4013 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 |
This theorem is referenced by: eufnfv 5616 abrexex 5983 ofmres 6002 difinfsn 6953 ctmlemr 6961 ctssdclemn0 6963 ctssdc 6966 enumct 6968 frec2uzrand 10146 frec2uzf1od 10147 frecfzennn 10167 uzennn 10177 0tonninf 10180 1tonninf 10181 hashinfom 10492 absval 10741 climle 11071 climcvg1nlem 11086 iserabs 11212 isumshft 11227 divcnv 11234 trireciplem 11237 expcnvap0 11239 expcnvre 11240 expcnv 11241 explecnv 11242 geolim 11248 geo2lim 11253 mertenslem2 11273 eftlub 11323 ctiunct 11880 restfn 12051 peano4nninf 13127 peano3nninf 13128 nninfsellemeq 13137 nninfsellemeqinf 13139 |
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