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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 5645 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2686 cmpt 3989 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-coll 4043 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 |
This theorem is referenced by: eufnfv 5648 abrexex 6015 ofmres 6034 difinfsn 6985 ctmlemr 6993 ctssdclemn0 6995 ctssdc 6998 enumct 7000 frec2uzrand 10178 frec2uzf1od 10179 frecfzennn 10199 uzennn 10209 0tonninf 10212 1tonninf 10213 hashinfom 10524 absval 10773 climle 11103 climcvg1nlem 11118 iserabs 11244 isumshft 11259 divcnv 11266 trireciplem 11269 expcnvap0 11271 expcnvre 11272 expcnv 11273 explecnv 11274 geolim 11280 geo2lim 11285 mertenslem2 11305 eftlub 11396 ctiunct 11953 restfn 12124 peano4nninf 13200 peano3nninf 13201 nninfsellemeq 13210 nninfsellemeqinf 13212 |
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