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Mirrors > Home > ILE Home > Th. List > ovmpog | Unicode version |
Description: Value of an operation given by a maps-to rule. Special case. (Contributed by NM, 14-Sep-1999.) (Revised by David Abernethy, 19-Jun-2012.) |
Ref | Expression |
---|---|
ovmpog.1 |
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ovmpog.2 |
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ovmpog.3 |
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Ref | Expression |
---|---|
ovmpog |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovmpog.1 |
. . 3
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2 | ovmpog.2 |
. . 3
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3 | 1, 2 | sylan9eq 2230 |
. 2
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4 | ovmpog.3 |
. 2
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5 | 3, 4 | ovmpoga 6003 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-setind 4536 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-iota 5178 df-fun 5218 df-fv 5224 df-ov 5877 df-oprab 5878 df-mpo 5879 |
This theorem is referenced by: ovmpo 6009 oav 6454 omv 6455 oeiv 6456 mapvalg 6657 pmvalg 6658 mulpipq2 7369 genipv 7507 genpelxp 7509 subval 8148 divvalap 8630 cnref1o 9649 modqval 10323 frecuzrdgrrn 10407 frec2uzrdg 10408 frecuzrdgrcl 10409 frecuzrdgsuc 10413 frecuzrdgrclt 10414 frecuzrdgg 10415 frecuzrdgsuctlem 10422 seq3val 10457 seqvalcd 10458 seqf 10460 seq3p1 10461 seqovcd 10462 seqp1cd 10465 exp3val 10521 bcval 10728 shftfvalg 10826 shftfval 10829 cnrecnv 10918 gcdval 11959 sqpweven 12174 2sqpwodd 12175 ennnfonelemp1 12406 nninfdclemcl 12448 nninfdclemp1 12450 ressvalsets 12523 imasex 12725 releqgg 13078 cnprcl2k 13676 xmetxp 13977 cncfval 14029 rpcxpef 14285 rplogbval 14333 |
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