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Mirrors > Home > ILE Home > Th. List > ftp | Unicode version |
Description: A function with a domain of three elements. (Contributed by Stefan O'Rear, 17-Oct-2014.) (Proof shortened by Alexander van der Vekens, 23-Jan-2018.) |
Ref | Expression |
---|---|
ftp.a | |
ftp.b | |
ftp.c | |
ftp.d | |
ftp.e | |
ftp.f | |
ftp.g | |
ftp.h | |
ftp.i |
Ref | Expression |
---|---|
ftp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ftp.a | . . 3 | |
2 | ftp.b | . . 3 | |
3 | ftp.c | . . 3 | |
4 | 1, 2, 3 | 3pm3.2i 1116 | . 2 |
5 | ftp.d | . . 3 | |
6 | ftp.e | . . 3 | |
7 | ftp.f | . . 3 | |
8 | 5, 6, 7 | 3pm3.2i 1116 | . 2 |
9 | ftp.g | . . 3 | |
10 | ftp.h | . . 3 | |
11 | ftp.i | . . 3 | |
12 | 9, 10, 11 | 3pm3.2i 1116 | . 2 |
13 | ftpg 5368 | . 2 | |
14 | 4, 8, 12, 13 | mp3an 1268 | 1 |
Colors of variables: wff set class |
Syntax hints: w3a 919 wcel 1433 wne 2245 cvv 2601 ctp 3400 cop 3401 wf 4918 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-reu 2355 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-tp 3406 df-op 3407 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 |
This theorem is referenced by: (None) |
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