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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 5170 | . . . . 5 |
6 | funtp.3 | . . . . . 6 | |
7 | funtp.6 | . . . . . 6 | |
8 | 6, 7 | funsn 5166 | . . . . 5 |
9 | 5, 8 | jctir 311 | . . . 4 |
10 | 3, 4 | dmprop 5008 | . . . . . . 7 |
11 | df-pr 3529 | . . . . . . 7 | |
12 | 10, 11 | eqtri 2158 | . . . . . 6 |
13 | 7 | dmsnop 5007 | . . . . . 6 |
14 | 12, 13 | ineq12i 3270 | . . . . 5 |
15 | disjsn2 3581 | . . . . . . 7 | |
16 | disjsn2 3581 | . . . . . . 7 | |
17 | 15, 16 | anim12i 336 | . . . . . 6 |
18 | undisj1 3415 | . . . . . 6 | |
19 | 17, 18 | sylib 121 | . . . . 5 |
20 | 14, 19 | syl5eq 2182 | . . . 4 |
21 | funun 5162 | . . . 4 | |
22 | 9, 20, 21 | syl2an 287 | . . 3 |
23 | 22 | 3impb 1177 | . 2 |
24 | df-tp 3530 | . . 3 | |
25 | 24 | funeqi 5139 | . 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 2306 cvv 2681 cun 3064 cin 3065 c0 3358 csn 3522 cpr 3523 ctp 3524 cop 3525 cdm 4534 wfun 5112 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
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 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-rex 2420 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-pw 3507 df-sn 3528 df-pr 3529 df-tp 3530 df-op 3531 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-fun 5120 |
This theorem is referenced by: fntp 5175 |
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