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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > polvalN | Structured version Visualization version Unicode version |
Description: Value of the projective subspace polarity function. (Contributed by NM, 23-Oct-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
polfval.o |
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polfval.a |
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polfval.m |
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polfval.p |
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Ref | Expression |
---|---|
polvalN |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | polfval.a |
. . . 4
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2 | fvex 5875 |
. . . 4
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3 | 1, 2 | eqeltri 2525 |
. . 3
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4 | 3 | elpw2 4567 |
. 2
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5 | polfval.o |
. . . . 5
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6 | polfval.m |
. . . . 5
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7 | polfval.p |
. . . . 5
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8 | 5, 1, 6, 7 | polfvalN 33469 |
. . . 4
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9 | 8 | fveq1d 5867 |
. . 3
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10 | iineq1 4293 |
. . . . 5
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11 | 10 | ineq2d 3634 |
. . . 4
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12 | eqid 2451 |
. . . 4
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13 | 3 | inex1 4544 |
. . . 4
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14 | 11, 12, 13 | fvmpt 5948 |
. . 3
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15 | 9, 14 | sylan9eq 2505 |
. 2
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16 | 4, 15 | 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-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-iun 4280 df-iin 4281 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-polarityN 33468 |
This theorem is referenced by: polval2N 33471 pol0N 33474 polcon3N 33482 polatN 33496 |
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