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Mirrors > Home > MPE Home > Th. List > Mathboxes > cvrval2 | Structured version Visualization version Unicode version |
Description: Binary relation
expressing ![]() ![]() |
Ref | Expression |
---|---|
cvrletr.b |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cvrletr.l |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cvrletr.s |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cvrletr.c |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
cvrval2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvrletr.b |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | cvrletr.s |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | cvrletr.c |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | cvrval 32829 |
. 2
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5 | iman 426 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | df-ne 2623 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | anbi2i 699 |
. . . . . . . 8
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8 | 5, 7 | xchbinxr 313 |
. . . . . . 7
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9 | cvrletr.l |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9, 2 | pltval 16199 |
. . . . . . . . . . . 12
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11 | 10 | 3com23 1213 |
. . . . . . . . . . 11
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12 | 11 | 3expa 1207 |
. . . . . . . . . 10
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13 | 12 | anbi2d 709 |
. . . . . . . . 9
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14 | anass 654 |
. . . . . . . . 9
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15 | 13, 14 | syl6rbbr 268 |
. . . . . . . 8
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16 | 15 | notbid 296 |
. . . . . . 7
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17 | 8, 16 | syl5bb 261 |
. . . . . 6
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18 | 17 | ralbidva 2823 |
. . . . 5
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19 | ralnex 2833 |
. . . . 5
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20 | 18, 19 | syl6bb 265 |
. . . 4
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21 | 20 | anbi2d 709 |
. . 3
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22 | 21 | 3adant2 1026 |
. 2
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23 | 4, 22 | bitr4d 260 |
1
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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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 ax-un 6580 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-mpt 4462 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-iota 5545 df-fun 5583 df-fv 5589 df-plt 16197 df-covers 32826 |
This theorem is referenced by: isat3 32867 cvlcvr1 32899 |
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