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Mirrors > Home > ILE Home > Th. List > fmpo | Unicode version |
Description: Functionality, domain and range of a class given by the maps-to notation. (Contributed by FL, 17-May-2010.) |
Ref | Expression |
---|---|
fmpo.1 |
Ref | Expression |
---|---|
fmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmpo.1 | . . 3 | |
2 | 1 | fmpox 6098 | . 2 |
3 | iunxpconst 4599 | . . 3 | |
4 | 3 | feq2i 5266 | . 2 |
5 | 2, 4 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 wral 2416 csn 3527 ciun 3813 cxp 4537 wf 5119 cmpo 5776 |
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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
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-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-fv 5131 df-oprab 5778 df-mpo 5779 df-1st 6038 df-2nd 6039 |
This theorem is referenced by: fnmpo 6100 ovmpoelrn 6105 fmpoco 6113 eroprf 6522 mapxpen 6742 subf 7967 xaddf 9630 ixxf 9684 ioof 9757 fzf 9797 fzof 9924 gcdf 11664 eucalgf 11739 txuni2 12428 txbasval 12439 cnmpt12 12459 cnmpt21 12463 cnmpt2t 12465 cnmpt22 12466 cnmptcom 12470 txswaphmeo 12493 blfvalps 12557 blfps 12581 blf 12582 bdmet 12674 xmetxp 12679 |
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