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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dihvalrel | Structured version Visualization version Unicode version |
Description: The value of isomorphism H is a relation. (Contributed by NM, 9-Mar-2014.) |
Ref | Expression |
---|---|
dihvalrel.h |
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dihvalrel.i |
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Ref | Expression |
---|---|
dihvalrel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2450 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | dihvalrel.h |
. . . . 5
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3 | dihvalrel.i |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | dihdm 34831 |
. . . 4
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5 | 4 | eleq2d 2513 |
. . 3
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6 | eqid 2450 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | eqid 2450 |
. . . . . . . 8
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8 | 1, 2, 3, 6, 7 | dihss 34813 |
. . . . . . 7
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9 | eqid 2450 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | eqid 2450 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 2, 9, 10, 6, 7 | dvhvbase 34649 |
. . . . . . . 8
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12 | 11 | adantr 467 |
. . . . . . 7
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13 | 8, 12 | sseqtrd 3467 |
. . . . . 6
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14 | xpss 4940 |
. . . . . 6
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15 | 13, 14 | syl6ss 3443 |
. . . . 5
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16 | df-rel 4840 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 15, 16 | sylibr 216 |
. . . 4
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18 | 17 | ex 436 |
. . 3
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19 | 5, 18 | sylbid 219 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | rel0 4957 |
. . 3
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21 | ndmfv 5887 |
. . . 4
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22 | 21 | releqd 4918 |
. . 3
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23 | 20, 22 | mpbiri 237 |
. 2
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24 | 19, 23 | pm2.61d1 163 |
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-rep 4514 ax-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 ax-un 6580 ax-cnex 9592 ax-resscn 9593 ax-1cn 9594 ax-icn 9595 ax-addcl 9596 ax-addrcl 9597 ax-mulcl 9598 ax-mulrcl 9599 ax-mulcom 9600 ax-addass 9601 ax-mulass 9602 ax-distr 9603 ax-i2m1 9604 ax-1ne0 9605 ax-1rid 9606 ax-rnegex 9607 ax-rrecex 9608 ax-cnre 9609 ax-pre-lttri 9610 ax-pre-lttrn 9611 ax-pre-ltadd 9612 ax-pre-mulgt0 9613 ax-riotaBAD 32519 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 985 df-3an 986 df-tru 1446 df-fal 1449 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-nel 2624 df-ral 2741 df-rex 2742 df-reu 2743 df-rmo 2744 df-rab 2745 df-v 3046 df-sbc 3267 df-csb 3363 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-pss 3419 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-tp 3972 df-op 3974 df-uni 4198 df-int 4234 df-iun 4279 df-iin 4280 df-br 4402 df-opab 4461 df-mpt 4462 df-tr 4497 df-eprel 4744 df-id 4748 df-po 4754 df-so 4755 df-fr 4792 df-we 4794 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-pred 5379 df-ord 5425 df-on 5426 df-lim 5427 df-suc 5428 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-f1 5586 df-fo 5587 df-f1o 5588 df-fv 5589 df-riota 6250 df-ov 6291 df-oprab 6292 df-mpt2 6293 df-om 6690 df-1st 6790 df-2nd 6791 df-tpos 6970 df-undef 7017 df-wrecs 7025 df-recs 7087 df-rdg 7125 df-1o 7179 df-oadd 7183 df-er 7360 df-map 7471 df-en 7567 df-dom 7568 df-sdom 7569 df-fin 7570 df-pnf 9674 df-mnf 9675 df-xr 9676 df-ltxr 9677 df-le 9678 df-sub 9859 df-neg 9860 df-nn 10607 df-2 10665 df-3 10666 df-4 10667 df-5 10668 df-6 10669 df-n0 10867 df-z 10935 df-uz 11157 df-fz 11782 df-struct 15116 df-ndx 15117 df-slot 15118 df-base 15119 df-sets 15120 df-ress 15121 df-plusg 15196 df-mulr 15197 df-sca 15199 df-vsca 15200 df-0g 15333 df-preset 16166 df-poset 16184 df-plt 16197 df-lub 16213 df-glb 16214 df-join 16215 df-meet 16216 df-p0 16278 df-p1 16279 df-lat 16285 df-clat 16347 df-mgm 16481 df-sgrp 16520 df-mnd 16530 df-submnd 16576 df-grp 16666 df-minusg 16667 df-sbg 16668 df-subg 16807 df-cntz 16964 df-lsm 17281 df-cmn 17425 df-abl 17426 df-mgp 17717 df-ur 17729 df-ring 17775 df-oppr 17844 df-dvdsr 17862 df-unit 17863 df-invr 17893 df-dvr 17904 df-drng 17970 df-lmod 18086 df-lss 18149 df-lsp 18188 df-lvec 18319 df-oposet 32736 df-ol 32738 df-oml 32739 df-covers 32826 df-ats 32827 df-atl 32858 df-cvlat 32882 df-hlat 32911 df-llines 33057 df-lplanes 33058 df-lvols 33059 df-lines 33060 df-psubsp 33062 df-pmap 33063 df-padd 33355 df-lhyp 33547 df-laut 33548 df-ldil 33663 df-ltrn 33664 df-trl 33719 df-tendo 34316 df-edring 34318 df-disoa 34591 df-dvech 34641 df-dib 34701 df-dic 34735 df-dih 34791 |
This theorem is referenced by: dih1 34848 dihmeetlem1N 34852 dihglblem5apreN 34853 dihglbcpreN 34862 dihmeetlem4preN 34868 dihmeetlem13N 34881 dihjatcclem4 34983 |
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