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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 6004 |
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 4122 ax-pow 4175 ax-pr 4210 ax-setind 4537 |
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 2740 df-sbc 2964 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-opab 4066 df-id 4294 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-iota 5179 df-fun 5219 df-fv 5225 df-ov 5878 df-oprab 5879 df-mpo 5880 |
This theorem is referenced by: ovmpo 6010 oav 6455 omv 6456 oeiv 6457 mapvalg 6658 pmvalg 6659 mulpipq2 7370 genipv 7508 genpelxp 7510 subval 8149 divvalap 8631 cnref1o 9650 modqval 10324 frecuzrdgrrn 10408 frec2uzrdg 10409 frecuzrdgrcl 10410 frecuzrdgsuc 10414 frecuzrdgrclt 10415 frecuzrdgg 10416 frecuzrdgsuctlem 10423 seq3val 10458 seqvalcd 10459 seqf 10461 seq3p1 10462 seqovcd 10463 seqp1cd 10466 exp3val 10522 bcval 10729 shftfvalg 10827 shftfval 10830 cnrecnv 10919 gcdval 11960 sqpweven 12175 2sqpwodd 12176 ennnfonelemp1 12407 nninfdclemcl 12449 nninfdclemp1 12451 ressvalsets 12524 imasex 12726 releqgg 13080 cnprcl2k 13709 xmetxp 14010 cncfval 14062 rpcxpef 14318 rplogbval 14366 |
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