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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 1082 | . 2 |
5 | ftp.d | . . 3 | |
6 | ftp.e | . . 3 | |
7 | ftp.f | . . 3 | |
8 | 5, 6, 7 | 3pm3.2i 1082 | . 2 |
9 | ftp.g | . . 3 | |
10 | ftp.h | . . 3 | |
11 | ftp.i | . . 3 | |
12 | 9, 10, 11 | 3pm3.2i 1082 | . 2 |
13 | ftpg 5347 | . 2 | |
14 | 4, 8, 12, 13 | mp3an 1232 | 1 |
Colors of variables: wff set class |
Syntax hints: w3a 885 wcel 1393 wne 2204 cvv 2557 ctp 3377 cop 3378 wf 4898 |
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-reu 2313 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-rn 4356 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 |
This theorem is referenced by: (None) |
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