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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 5878 |
. 2
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2 | eqid 2177 |
. . . . . 6
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3 | biidd 172 |
. . . . . . 7
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4 | 3 | copsex2g 4247 |
. . . . . 6
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5 | 2, 4 | mpbiri 168 |
. . . . 5
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6 | 5 | 3adant3 1017 |
. . . 4
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7 | 6 | adantr 276 |
. . 3
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8 | eqeq1 2184 |
. . . . . . . 8
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9 | 8 | anbi1d 465 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | ov6g.1 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | eqeq2d 2189 |
. . . . . . . . 9
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12 | 11 | eqcoms 2180 |
. . . . . . . 8
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13 | 12 | pm5.32i 454 |
. . . . . . 7
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14 | 9, 13 | bitrdi 196 |
. . . . . 6
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15 | 14 | 2exbidv 1868 |
. . . . 5
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16 | eqeq1 2184 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 16 | anbi2d 464 |
. . . . . 6
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18 | 17 | 2exbidv 1868 |
. . . . 5
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19 | moeq 2913 |
. . . . . . 7
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20 | 19 | mosubop 4693 |
. . . . . 6
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21 | 20 | a1i 9 |
. . . . 5
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22 | ov6g.2 |
. . . . . 6
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23 | dfoprab2 5922 |
. . . . . 6
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24 | eleq1 2240 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 24 | anbi1d 465 |
. . . . . . . . . . 11
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26 | 25 | pm5.32i 454 |
. . . . . . . . . 10
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27 | an12 561 |
. . . . . . . . . 10
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28 | 26, 27 | bitr3i 186 |
. . . . . . . . 9
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29 | 28 | 2exbii 1606 |
. . . . . . . 8
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30 | 19.42vv 1911 |
. . . . . . . 8
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31 | 29, 30 | bitri 184 |
. . . . . . 7
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32 | 31 | opabbii 4071 |
. . . . . 6
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33 | 22, 23, 32 | 3eqtri 2202 |
. . . . 5
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34 | 15, 18, 21, 33 | fvopab3ig 5591 |
. . . 4
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35 | 34 | 3ad2antl3 1161 |
. . 3
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36 | 7, 35 | mpd 13 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | 1, 36 | eqtrid 2222 |
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 106 ax-ia2 107 ax-ia3 108 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 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 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-ral 2460 df-rex 2461 df-v 2740 df-sbc 2964 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 |
This theorem is referenced by: (None) |
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