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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > pclvalN | Structured version Visualization version Unicode version |
Description: Value of the projective subspace closure function. (Contributed by NM, 7-Sep-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pclfval.a |
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pclfval.s |
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pclfval.c |
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Ref | Expression |
---|---|
pclvalN |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pclfval.a |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | fvex 5875 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | eqeltri 2525 |
. . 3
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4 | 3 | elpw2 4567 |
. 2
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5 | pclfval.s |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | pclfval.c |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 1, 5, 6 | pclfvalN 33454 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | fveq1d 5867 |
. . . 4
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9 | 8 | adantr 467 |
. . 3
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10 | simpr 463 |
. . . 4
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11 | elpwi 3960 |
. . . . . . . 8
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12 | 11 | adantl 468 |
. . . . . . 7
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13 | 1, 5 | atpsubN 33318 |
. . . . . . . . 9
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14 | 13 | adantr 467 |
. . . . . . . 8
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15 | sseq2 3454 |
. . . . . . . . 9
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16 | 15 | elrab3 3197 |
. . . . . . . 8
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17 | 14, 16 | syl 17 |
. . . . . . 7
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18 | 12, 17 | mpbird 236 |
. . . . . 6
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19 | ne0i 3737 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 18, 19 | syl 17 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | intex 4559 |
. . . . 5
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22 | 20, 21 | sylib 200 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | sseq1 3453 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23 | rabbidv 3036 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | inteqd 4239 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | eqid 2451 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | 25, 26 | fvmptg 5946 |
. . . 4
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28 | 10, 22, 27 | syl2anc 667 |
. . 3
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29 | 9, 28 | eqtrd 2485 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 4, 29 | sylan2br 479 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-int 4235 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-ov 6293 df-psubsp 33068 df-pclN 33453 |
This theorem is referenced by: pclclN 33456 elpclN 33457 elpcliN 33458 pclssN 33459 pclssidN 33460 pclidN 33461 |
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