Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > chfnrn | Unicode version |
Description: The range of a choice function (a function that chooses an element from each member of its domain) is included in the union of its domain. (Contributed by NM, 31-Aug-1999.) |
Ref | Expression |
---|---|
chfnrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvelrnb 5221 | . . . . 5 | |
2 | 1 | biimpd 132 | . . . 4 |
3 | eleq1 2100 | . . . . . . 7 | |
4 | 3 | biimpcd 148 | . . . . . 6 |
5 | 4 | ralimi 2384 | . . . . 5 |
6 | rexim 2413 | . . . . 5 | |
7 | 5, 6 | syl 14 | . . . 4 |
8 | 2, 7 | sylan9 389 | . . 3 |
9 | eluni2 3584 | . . 3 | |
10 | 8, 9 | syl6ibr 151 | . 2 |
11 | 10 | ssrdv 2951 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 wral 2306 wrex 2307 wss 2917 cuni 3580 crn 4346 wfn 4897 cfv 4902 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-iota 4867 df-fun 4904 df-fn 4905 df-fv 4910 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |