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Mirrors > Home > ILE Home > Th. List > fmptd | Unicode version |
Description: Domain and codomain of the mapping operation; deduction form. (Contributed by Mario Carneiro, 13-Jan-2013.) |
Ref | Expression |
---|---|
fmptd.1 | |
fmptd.2 |
Ref | Expression |
---|---|
fmptd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmptd.1 | . . 3 | |
2 | 1 | ralrimiva 2482 | . 2 |
3 | fmptd.2 | . . 3 | |
4 | 3 | fmpt 5538 | . 2 |
5 | 2, 4 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 wral 2393 cmpt 3959 wf 5089 |
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-rab 2402 df-v 2662 df-sbc 2883 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-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-fv 5101 |
This theorem is referenced by: fmpttd 5543 fmptco 5554 fliftrel 5661 off 5962 caofinvl 5972 fdiagfn 6554 mapxpen 6710 xpmapenlem 6711 updjudhf 6932 enumctlemm 6967 fodjuf 6985 nnnninf 6991 caucvgsrlemf 7568 caucvgsrlemofff 7573 axcaucvglemf 7672 monoord2 10218 iseqf1olemqf 10232 cvg1nlemf 10723 resqrexlemsqa 10764 climcvg1nlem 11086 summodclem2a 11118 crth 11827 ctiunctlemf 11878 txcnmpt 12369 txlm 12375 mulc1cncf 12672 addccncf 12682 negcncf 12684 nnsf 13126 nninfself 13136 |
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