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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 2193 |
. 2
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4 | ovmpog.3 |
. 2
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5 | 3, 4 | ovmpoga 5908 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-setind 4460 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-ov 5785 df-oprab 5786 df-mpo 5787 |
This theorem is referenced by: ovmpo 5914 oav 6358 omv 6359 oeiv 6360 mapvalg 6560 pmvalg 6561 mulpipq2 7203 genipv 7341 genpelxp 7343 subval 7978 divvalap 8458 cnref1o 9469 modqval 10128 frecuzrdgrrn 10212 frec2uzrdg 10213 frecuzrdgrcl 10214 frecuzrdgsuc 10218 frecuzrdgrclt 10219 frecuzrdgg 10220 frecuzrdgsuctlem 10227 seq3val 10262 seqvalcd 10263 seqf 10265 seq3p1 10266 seqovcd 10267 seqp1cd 10270 exp3val 10326 bcval 10527 shftfvalg 10622 shftfval 10625 cnrecnv 10714 gcdval 11684 sqpweven 11889 2sqpwodd 11890 ennnfonelemp1 11955 cnprcl2k 12414 xmetxp 12715 cncfval 12767 rpcxpef 13023 rplogbval 13070 |
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