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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 1159 | . 2 |
5 | ftp.d | . . 3 | |
6 | ftp.e | . . 3 | |
7 | ftp.f | . . 3 | |
8 | 5, 6, 7 | 3pm3.2i 1159 | . 2 |
9 | ftp.g | . . 3 | |
10 | ftp.h | . . 3 | |
11 | ftp.i | . . 3 | |
12 | 9, 10, 11 | 3pm3.2i 1159 | . 2 |
13 | ftpg 5597 | . 2 | |
14 | 4, 8, 12, 13 | mp3an 1315 | 1 |
Colors of variables: wff set class |
Syntax hints: w3a 962 wcel 1480 wne 2306 cvv 2681 ctp 3524 cop 3525 wf 5114 |
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-reu 2421 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-rn 4545 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 |
This theorem is referenced by: (None) |
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