Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ftpg | Unicode version |
Description: A function with a domain of three elements. (Contributed by Alexander van der Vekens, 4-Dec-2017.) |
Ref | Expression |
---|---|
ftpg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simpa 978 | . . . 4 | |
2 | 3simpa 978 | . . . 4 | |
3 | simp1 981 | . . . 4 | |
4 | fprg 5596 | . . . 4 | |
5 | 1, 2, 3, 4 | syl3an 1258 | . . 3 |
6 | eqidd 2138 | . . . 4 | |
7 | simp3 983 | . . . . . . 7 | |
8 | simp3 983 | . . . . . . 7 | |
9 | 7, 8 | anim12i 336 | . . . . . 6 |
10 | 9 | 3adant3 1001 | . . . . 5 |
11 | fsng 5586 | . . . . 5 | |
12 | 10, 11 | syl 14 | . . . 4 |
13 | 6, 12 | mpbird 166 | . . 3 |
14 | df-ne 2307 | . . . . . . 7 | |
15 | df-ne 2307 | . . . . . . 7 | |
16 | elpri 3545 | . . . . . . . . . 10 | |
17 | eqcom 2139 | . . . . . . . . . . 11 | |
18 | eqcom 2139 | . . . . . . . . . . 11 | |
19 | 17, 18 | orbi12i 753 | . . . . . . . . . 10 |
20 | 16, 19 | sylib 121 | . . . . . . . . 9 |
21 | oranim 770 | . . . . . . . . 9 | |
22 | 20, 21 | syl 14 | . . . . . . . 8 |
23 | 22 | con2i 616 | . . . . . . 7 |
24 | 14, 15, 23 | syl2anb 289 | . . . . . 6 |
25 | 24 | 3adant1 999 | . . . . 5 |
26 | 25 | 3ad2ant3 1004 | . . . 4 |
27 | disjsn 3580 | . . . 4 | |
28 | 26, 27 | sylibr 133 | . . 3 |
29 | fun 5290 | . . 3 | |
30 | 5, 13, 28, 29 | syl21anc 1215 | . 2 |
31 | df-tp 3530 | . . . 4 | |
32 | 31 | feq1i 5260 | . . 3 |
33 | df-tp 3530 | . . . 4 | |
34 | df-tp 3530 | . . . 4 | |
35 | 33, 34 | feq23i 5262 | . . 3 |
36 | 32, 35 | bitri 183 | . 2 |
37 | 30, 36 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 697 w3a 962 wceq 1331 wcel 1480 wne 2306 cun 3064 cin 3065 c0 3358 csn 3522 cpr 3523 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: ftp 5598 |
Copyright terms: Public domain | W3C validator |