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Mirrors > Home > ILE Home > Th. List > ov6g | Unicode version |
Description: The value of an operation class abstraction. Special case. (Contributed by NM, 13-Nov-2006.) |
Ref | Expression |
---|---|
ov6g.1 |
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ov6g.2 |
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Ref | Expression |
---|---|
ov6g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5785 |
. 2
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2 | eqid 2140 |
. . . . . 6
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3 | biidd 171 |
. . . . . . 7
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4 | 3 | copsex2g 4176 |
. . . . . 6
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5 | 2, 4 | mpbiri 167 |
. . . . 5
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6 | 5 | 3adant3 1002 |
. . . 4
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7 | 6 | adantr 274 |
. . 3
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8 | eqeq1 2147 |
. . . . . . . 8
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9 | 8 | anbi1d 461 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | ov6g.1 |
. . . . . . . . . 10
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11 | 10 | eqeq2d 2152 |
. . . . . . . . 9
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12 | 11 | eqcoms 2143 |
. . . . . . . 8
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13 | 12 | pm5.32i 450 |
. . . . . . 7
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14 | 9, 13 | syl6bb 195 |
. . . . . 6
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15 | 14 | 2exbidv 1841 |
. . . . 5
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16 | eqeq1 2147 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 16 | anbi2d 460 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 17 | 2exbidv 1841 |
. . . . 5
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19 | moeq 2863 |
. . . . . . 7
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20 | 19 | mosubop 4613 |
. . . . . 6
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21 | 20 | a1i 9 |
. . . . 5
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22 | ov6g.2 |
. . . . . 6
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23 | dfoprab2 5826 |
. . . . . 6
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24 | eleq1 2203 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 24 | anbi1d 461 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25 | pm5.32i 450 |
. . . . . . . . . 10
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27 | an12 551 |
. . . . . . . . . 10
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28 | 26, 27 | bitr3i 185 |
. . . . . . . . 9
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29 | 28 | 2exbii 1586 |
. . . . . . . 8
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30 | 19.42vv 1884 |
. . . . . . . 8
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31 | 29, 30 | bitri 183 |
. . . . . . 7
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32 | 31 | opabbii 4003 |
. . . . . 6
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33 | 22, 23, 32 | 3eqtri 2165 |
. . . . 5
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34 | 15, 18, 21, 33 | fvopab3ig 5503 |
. . . 4
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35 | 34 | 3ad2antl3 1146 |
. . 3
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36 | 7, 35 | mpd 13 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | 1, 36 | syl5eq 2185 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-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 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 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-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 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 |
This theorem is referenced by: (None) |
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