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Mirrors > Home > MPE Home > Th. List > ov6g | Structured version Visualization version 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 6318 |
. 2
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2 | eqid 2462 |
. . . . . 6
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3 | biidd 245 |
. . . . . . 7
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4 | 3 | copsex2g 4703 |
. . . . . 6
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5 | 2, 4 | mpbiri 241 |
. . . . 5
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6 | 5 | 3adant3 1034 |
. . . 4
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7 | 6 | adantr 471 |
. . 3
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8 | eqeq1 2466 |
. . . . . . . 8
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9 | 8 | anbi1d 716 |
. . . . . . 7
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10 | ov6g.1 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | eqeq2d 2472 |
. . . . . . . . 9
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12 | 11 | eqcoms 2470 |
. . . . . . . 8
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13 | 12 | pm5.32i 647 |
. . . . . . 7
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14 | 9, 13 | syl6bb 269 |
. . . . . 6
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15 | 14 | 2exbidv 1781 |
. . . . 5
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16 | eqeq1 2466 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 16 | anbi2d 715 |
. . . . . 6
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18 | 17 | 2exbidv 1781 |
. . . . 5
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19 | moeq 3226 |
. . . . . . 7
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20 | 19 | mosubop 4714 |
. . . . . 6
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21 | 20 | a1i 11 |
. . . . 5
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22 | ov6g.2 |
. . . . . 6
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23 | dfoprab2 6364 |
. . . . . 6
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24 | eleq1 2528 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 24 | anbi1d 716 |
. . . . . . . . . . 11
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26 | 25 | pm5.32i 647 |
. . . . . . . . . 10
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27 | an12 811 |
. . . . . . . . . 10
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28 | 26, 27 | bitr3i 259 |
. . . . . . . . 9
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29 | 28 | 2exbii 1730 |
. . . . . . . 8
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30 | 19.42vv 1847 |
. . . . . . . 8
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31 | 29, 30 | bitri 257 |
. . . . . . 7
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32 | 31 | opabbii 4481 |
. . . . . 6
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33 | 22, 23, 32 | 3eqtri 2488 |
. . . . 5
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34 | 15, 18, 21, 33 | fvopab3ig 5968 |
. . . 4
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35 | 34 | 3ad2antl3 1178 |
. . 3
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36 | 7, 35 | mpd 15 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | 1, 36 | syl5eq 2508 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-sbc 3280 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4417 df-opab 4476 df-id 4768 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-iota 5565 df-fun 5603 df-fv 5609 df-ov 6318 df-oprab 6319 |
This theorem is referenced by: (None) |
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