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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dibf11N | Structured version Unicode version |
Description: The partial isomorphism A
for a lattice ![]() |
Ref | Expression |
---|---|
dibcl.h |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dibcl.i |
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Ref | Expression |
---|---|
dibf11N |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2452 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | eqid 2452 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | dibcl.h |
. . . 4
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4 | dibcl.i |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | dibfnN 35120 |
. . 3
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6 | fnfun 5611 |
. . . 4
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7 | funfn 5550 |
. . . 4
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8 | 6, 7 | sylib 196 |
. . 3
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9 | 5, 8 | syl 16 |
. 2
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10 | eqidd 2453 |
. 2
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11 | 1, 2, 3, 4 | dibeldmN 35122 |
. . . . 5
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12 | 1, 2, 3, 4 | dibeldmN 35122 |
. . . . 5
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13 | 11, 12 | anbi12d 710 |
. . . 4
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14 | 1, 2, 3, 4 | dib11N 35124 |
. . . . . 6
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15 | 14 | biimpd 207 |
. . . . 5
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16 | 15 | 3expib 1191 |
. . . 4
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17 | 13, 16 | sylbid 215 |
. . 3
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18 | 17 | ralrimivv 2907 |
. 2
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19 | dff1o6 6086 |
. 2
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20 | 9, 10, 18, 19 | syl3anbrc 1172 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 ax-rep 4506 ax-sep 4516 ax-nul 4524 ax-pow 4573 ax-pr 4634 ax-un 6477 ax-riotaBAD 32923 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2265 df-mo 2266 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ne 2647 df-nel 2648 df-ral 2801 df-rex 2802 df-reu 2803 df-rmo 2804 df-rab 2805 df-v 3074 df-sbc 3289 df-csb 3391 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-nul 3741 df-if 3895 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4195 df-iun 4276 df-iin 4277 df-br 4396 df-opab 4454 df-mpt 4455 df-id 4739 df-xp 4949 df-rel 4950 df-cnv 4951 df-co 4952 df-dm 4953 df-rn 4954 df-res 4955 df-ima 4956 df-iota 5484 df-fun 5523 df-fn 5524 df-f 5525 df-f1 5526 df-fo 5527 df-f1o 5528 df-fv 5529 df-riota 6156 df-ov 6198 df-oprab 6199 df-mpt2 6200 df-1st 6682 df-2nd 6683 df-undef 6897 df-map 7321 df-poset 15230 df-plt 15242 df-lub 15258 df-glb 15259 df-join 15260 df-meet 15261 df-p0 15323 df-p1 15324 df-lat 15330 df-clat 15392 df-oposet 33140 df-ol 33142 df-oml 33143 df-covers 33230 df-ats 33231 df-atl 33262 df-cvlat 33286 df-hlat 33315 df-llines 33461 df-lplanes 33462 df-lvols 33463 df-lines 33464 df-psubsp 33466 df-pmap 33467 df-padd 33759 df-lhyp 33951 df-laut 33952 df-ldil 34067 df-ltrn 34068 df-trl 34122 df-disoa 34993 df-dib 35103 |
This theorem is referenced by: dibintclN 35131 |
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