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Mirrors > Home > ILE Home > Th. List > f1ocnvfv2 | Unicode version |
Description: The value of the converse value of a one-to-one onto function. (Contributed by NM, 20-May-2004.) |
Ref | Expression |
---|---|
f1ocnvfv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ococnv2 5441 | . . . 4 | |
2 | 1 | fveq1d 5470 | . . 3 |
3 | 2 | adantr 274 | . 2 |
4 | f1ocnv 5427 | . . . 4 | |
5 | f1of 5414 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | fvco3 5539 | . . 3 | |
8 | 6, 7 | sylan 281 | . 2 |
9 | fvresi 5660 | . . 3 | |
10 | 9 | adantl 275 | . 2 |
11 | 3, 8, 10 | 3eqtr3d 2198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cid 4248 ccnv 4585 cres 4588 ccom 4590 wf 5166 wf1o 5169 cfv 5170 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-iota 5135 df-fun 5172 df-fn 5173 df-f 5174 df-f1 5175 df-fo 5176 df-f1o 5177 df-fv 5178 |
This theorem is referenced by: f1ocnvfvb 5730 isocnv 5761 f1oiso2 5777 ordiso2 6979 enomnilem 7081 enmkvlem 7104 enwomnilem 7112 frecuzrdglem 10310 frecuzrdgsuc 10313 frecuzrdgdomlem 10316 frecuzrdgsuctlem 10322 frecfzennn 10325 iseqf1olemkle 10383 iseqf1olemklt 10384 iseqf1olemnab 10387 seq3f1olemqsumkj 10397 hashfz1 10657 seq3coll 10713 summodclem3 11277 summodclem2a 11278 prodmodclem3 11472 prodmodclem2a 11473 sqpweven 12049 2sqpwodd 12050 phimullem 12099 eulerthlemth 12106 ennnfonelemkh 12141 ennnfonelemhf1o 12142 ennnfonelemex 12143 ennnfonelemnn0 12151 ctinfomlemom 12156 ctiunctlemfo 12168 reeflog 13184 isomninnlem 13601 iswomninnlem 13620 ismkvnnlem 13623 |
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