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Mirrors > Home > MPE Home > Th. List > f1ocnvfv1 | Structured version Visualization version Unicode version |
Description: The converse value of the value of a one-to-one onto function. (Contributed by NM, 20-May-2004.) |
Ref | Expression |
---|---|
f1ocnvfv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ococnv1 6165 | . . . 4 | |
2 | 1 | fveq1d 6193 | . . 3 |
3 | 2 | adantr 481 | . 2 |
4 | f1of 6137 | . . 3 | |
5 | fvco3 6275 | . . 3 | |
6 | 4, 5 | sylan 488 | . 2 |
7 | fvresi 6439 | . . 3 | |
8 | 7 | adantl 482 | . 2 |
9 | 3, 6, 8 | 3eqtr3d 2664 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cid 5023 ccnv 5113 cres 5116 ccom 5118 wf 5884 wf1o 5887 cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 |
This theorem is referenced by: f1ocnvfv 6534 wemapwe 8594 fseqenlem2 8848 acndom 8874 isf34lem5 9200 axcc3 9260 pwfseqlem1 9480 hashdom 13168 fz1isolem 13245 cnrecnv 13905 sadcadd 15180 sadadd2 15182 invinv 16430 catcisolem 16756 mhmf1o 17345 srngnvl 18856 mdetleib2 20394 2ndcdisj 21259 cnheiborlem 22753 iunmbl2 23325 dvcnvlem 23739 eff1olem 24294 logef 24328 adjbdlnb 28943 cnvbrabra 28971 fsumiunle 29575 fzto1stinvn 29854 madjusmdetlem1 29893 tpr2rico 29958 esumiun 30156 lautj 35379 lautm 35380 ldilcnv 35401 ltrneq2 35434 trlcnv 35452 diaocN 36414 dihcnvid1 36561 dochocss 36655 mapdcnvid1N 36943 |
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