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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 5704 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cvv 2721 cmpt 4037 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-coll 4091 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 df-fv 5190 |
This theorem is referenced by: mptrabex 5707 eufnfv 5709 abrexex 6077 ofmres 6096 difinfsn 7056 ctmlemr 7064 ctssdclemn0 7066 ctssdc 7069 enumct 7071 frec2uzrand 10330 frec2uzf1od 10331 frecfzennn 10351 uzennn 10361 0tonninf 10364 1tonninf 10365 hashinfom 10680 absval 10929 climle 11261 climcvg1nlem 11276 iserabs 11402 isumshft 11417 divcnv 11424 trireciplem 11427 expcnvap0 11429 expcnvre 11430 expcnv 11431 explecnv 11432 geolim 11438 geo2lim 11443 mertenslem2 11463 eftlub 11617 ctiunct 12316 restfn 12502 peano4nninf 13727 peano3nninf 13728 nninfsellemeq 13735 nninfsellemeqinf 13737 dceqnconst 13779 dcapnconst 13780 |
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