Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > funtp | Unicode version |
Description: A function with a domain of three elements. (Contributed by NM, 14-Sep-2011.) |
Ref | Expression |
---|---|
funtp.1 | |
funtp.2 | |
funtp.3 | |
funtp.4 | |
funtp.5 | |
funtp.6 |
Ref | Expression |
---|---|
funtp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funtp.1 | . . . . . 6 | |
2 | funtp.2 | . . . . . 6 | |
3 | funtp.4 | . . . . . 6 | |
4 | funtp.5 | . . . . . 6 | |
5 | 1, 2, 3, 4 | funpr 4951 | . . . . 5 |
6 | funtp.3 | . . . . . 6 | |
7 | funtp.6 | . . . . . 6 | |
8 | 6, 7 | funsn 4948 | . . . . 5 |
9 | 5, 8 | jctir 296 | . . . 4 |
10 | 3, 4 | dmprop 4795 | . . . . . . 7 |
11 | df-pr 3382 | . . . . . . 7 | |
12 | 10, 11 | eqtri 2060 | . . . . . 6 |
13 | 7 | dmsnop 4794 | . . . . . 6 |
14 | 12, 13 | ineq12i 3136 | . . . . 5 |
15 | disjsn2 3433 | . . . . . . 7 | |
16 | disjsn2 3433 | . . . . . . 7 | |
17 | 15, 16 | anim12i 321 | . . . . . 6 |
18 | undisj1 3279 | . . . . . 6 | |
19 | 17, 18 | sylib 127 | . . . . 5 |
20 | 14, 19 | syl5eq 2084 | . . . 4 |
21 | funun 4944 | . . . 4 | |
22 | 9, 20, 21 | syl2an 273 | . . 3 |
23 | 22 | 3impb 1100 | . 2 |
24 | df-tp 3383 | . . 3 | |
25 | 24 | funeqi 4922 | . 2 |
26 | 23, 25 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wcel 1393 wne 2204 cvv 2557 cun 2915 cin 2916 c0 3224 csn 3375 cpr 3376 ctp 3377 cop 3378 cdm 4345 wfun 4896 |
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-in1 544 ax-in2 545 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-fal 1249 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-ne 2206 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-nul 3225 df-pw 3361 df-sn 3381 df-pr 3382 df-tp 3383 df-op 3384 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-fun 4904 |
This theorem is referenced by: fntp 4956 |
Copyright terms: Public domain | W3C validator |