Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ndmima | Unicode version |
Description: The image of a singleton outside the domain is empty. (Contributed by NM, 22-May-1998.) |
Ref | Expression |
---|---|
ndmima |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 4522 | . 2 | |
2 | dmres 4810 | . . . . 5 | |
3 | incom 3238 | . . . . 5 | |
4 | 2, 3 | eqtri 2138 | . . . 4 |
5 | disjsn 3555 | . . . . 5 | |
6 | 5 | biimpri 132 | . . . 4 |
7 | 4, 6 | syl5eq 2162 | . . 3 |
8 | dm0rn0 4726 | . . 3 | |
9 | 7, 8 | sylib 121 | . 2 |
10 | 1, 9 | syl5eq 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1316 wcel 1465 cin 3040 c0 3333 csn 3497 cdm 4509 crn 4510 cres 4511 cima 4512 |
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-in1 588 ax-in2 589 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-fal 1322 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-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 |
This theorem is referenced by: fvun1 5455 |
Copyright terms: Public domain | W3C validator |