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Mirrors > Home > ILE Home > Th. List > funmpt | Unicode version |
Description: A function in maps-to notation is a function. (Contributed by Mario Carneiro, 13-Jan-2013.) |
Ref | Expression |
---|---|
funmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funopab4 5130 | . 2 | |
2 | df-mpt 3961 | . . 3 | |
3 | 2 | funeqi 5114 | . 2 |
4 | 1, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 wcel 1465 copab 3958 cmpt 3959 wfun 5087 |
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-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-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 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-fun 5095 |
This theorem is referenced by: funmpt2 5132 fmptco 5554 resfunexg 5609 mptexg 5613 brtpos2 6116 tposfun 6125 rdgtfr 6239 rdgruledefgg 6240 rdgon 6251 freccllem 6267 frecfcllem 6269 hashinfom 10492 hashennn 10494 negfi 10967 tgrest 12265 dvrecap 12773 |
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