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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 1144 | . 2 |
5 | ftp.d | . . 3 | |
6 | ftp.e | . . 3 | |
7 | ftp.f | . . 3 | |
8 | 5, 6, 7 | 3pm3.2i 1144 | . 2 |
9 | ftp.g | . . 3 | |
10 | ftp.h | . . 3 | |
11 | ftp.i | . . 3 | |
12 | 9, 10, 11 | 3pm3.2i 1144 | . 2 |
13 | ftpg 5572 | . 2 | |
14 | 4, 8, 12, 13 | mp3an 1300 | 1 |
Colors of variables: wff set class |
Syntax hints: w3a 947 wcel 1465 wne 2285 cvv 2660 ctp 3499 cop 3500 wf 5089 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-reu 2400 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-tp 3505 df-op 3506 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 |
This theorem is referenced by: (None) |
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