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Mirrors > Home > ILE Home > Th. List > ovmpoga | Unicode version |
Description: Value of an operation given by a maps-to rule. (Contributed by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ovmpoga.1 |
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ovmpoga.2 |
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Ref | Expression |
---|---|
ovmpoga |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. 2
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2 | ovmpoga.2 |
. . . 4
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3 | 2 | a1i 9 |
. . 3
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4 | ovmpoga.1 |
. . . 4
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5 | 4 | adantl 275 |
. . 3
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6 | simp1 982 |
. . 3
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7 | simp2 983 |
. . 3
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8 | simp3 984 |
. . 3
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9 | 3, 5, 6, 7, 8 | ovmpod 5906 |
. 2
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10 | 1, 9 | syl3an3 1252 |
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: ovmpoa 5909 ovmpog 5913 elovmpo 5979 offval 5997 offval3 6040 xaddval 9658 fzoval 9956 eucalgval2 11770 setsvalg 12028 ressid2 12057 ressval2 12058 restval 12165 txvalex 12462 txval 12463 cnmpt12 12495 cnmpt22 12502 hmeofvalg 12511 bdmetval 12708 xmetxp 12715 xmetxpbl 12716 txmetcnp 12726 limccl 12836 ellimc3apf 12837 |
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