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Mirrors > Home > ILE Home > Th. List > f1ocnv2d | Unicode version |
Description: Describe an implicit one-to-one onto function. (Contributed by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
f1od.1 | |
f1o2d.2 | |
f1o2d.3 | |
f1o2d.4 |
Ref | Expression |
---|---|
f1ocnv2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1od.1 | . 2 | |
2 | f1o2d.2 | . 2 | |
3 | f1o2d.3 | . 2 | |
4 | eleq1a 2236 | . . . . . 6 | |
5 | 2, 4 | syl 14 | . . . . 5 |
6 | 5 | impr 377 | . . . 4 |
7 | f1o2d.4 | . . . . . . . 8 | |
8 | 7 | biimpar 295 | . . . . . . 7 |
9 | 8 | exp42 369 | . . . . . 6 |
10 | 9 | com34 83 | . . . . 5 |
11 | 10 | imp32 255 | . . . 4 |
12 | 6, 11 | jcai 309 | . . 3 |
13 | eleq1a 2236 | . . . . . 6 | |
14 | 3, 13 | syl 14 | . . . . 5 |
15 | 14 | impr 377 | . . . 4 |
16 | 7 | biimpa 294 | . . . . . . . 8 |
17 | 16 | exp42 369 | . . . . . . 7 |
18 | 17 | com23 78 | . . . . . 6 |
19 | 18 | com34 83 | . . . . 5 |
20 | 19 | imp32 255 | . . . 4 |
21 | 15, 20 | jcai 309 | . . 3 |
22 | 12, 21 | impbida 586 | . 2 |
23 | 1, 2, 3, 22 | f1ocnvd 6034 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 cmpt 4037 ccnv 4597 wf1o 5181 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 |
This theorem is referenced by: f1o2d 6037 negf1o 8271 negiso 8841 iccf1o 9931 xrnegiso 11189 txhmeo 12860 |
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