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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 5175 | . . . . 5 |
6 | funtp.3 | . . . . . 6 | |
7 | funtp.6 | . . . . . 6 | |
8 | 6, 7 | funsn 5171 | . . . . 5 |
9 | 5, 8 | jctir 311 | . . . 4 |
10 | 3, 4 | dmprop 5013 | . . . . . . 7 |
11 | df-pr 3534 | . . . . . . 7 | |
12 | 10, 11 | eqtri 2160 | . . . . . 6 |
13 | 7 | dmsnop 5012 | . . . . . 6 |
14 | 12, 13 | ineq12i 3275 | . . . . 5 |
15 | disjsn2 3586 | . . . . . . 7 | |
16 | disjsn2 3586 | . . . . . . 7 | |
17 | 15, 16 | anim12i 336 | . . . . . 6 |
18 | undisj1 3420 | . . . . . 6 | |
19 | 17, 18 | sylib 121 | . . . . 5 |
20 | 14, 19 | syl5eq 2184 | . . . 4 |
21 | funun 5167 | . . . 4 | |
22 | 9, 20, 21 | syl2an 287 | . . 3 |
23 | 22 | 3impb 1177 | . 2 |
24 | df-tp 3535 | . . 3 | |
25 | 24 | funeqi 5144 | . 2 |
26 | 23, 25 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 wne 2308 cvv 2686 cun 3069 cin 3070 c0 3363 csn 3527 cpr 3528 ctp 3529 cop 3530 cdm 4539 wfun 5117 |
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 603 ax-in2 604 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-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 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 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-ne 2309 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-tp 3535 df-op 3536 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-fun 5125 |
This theorem is referenced by: fntp 5180 |
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