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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 5173 | . . . 4 | |
2 | 1 | fveq1d 5200 | . . 3 |
3 | 2 | adantr 270 | . 2 |
4 | f1ocnv 5159 | . . . 4 | |
5 | f1of 5146 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | fvco3 5265 | . . 3 | |
8 | 6, 7 | sylan 277 | . 2 |
9 | fvresi 5377 | . . 3 | |
10 | 9 | adantl 271 | . 2 |
11 | 3, 8, 10 | 3eqtr3d 2121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 cid 4043 ccnv 4362 cres 4365 ccom 4367 wf 4918 wf1o 4921 cfv 4922 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 |
This theorem is referenced by: f1ocnvfvb 5440 isocnv 5471 f1oiso2 5486 ordiso2 6446 frecuzrdglem 9413 frecuzrdgsuc 9417 frecfzennn 9419 sqpweven 10553 2sqpwodd 10554 |
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