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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > isline | Structured version Visualization version Unicode version |
Description: The predicate "is a line". (Contributed by NM, 19-Sep-2011.) |
Ref | Expression |
---|---|
isline.l |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
isline.j |
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isline.a |
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isline.n |
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Ref | Expression |
---|---|
isline |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isline.l |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | isline.j |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | isline.a |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | isline.n |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | lineset 33347 |
. . 3
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6 | 5 | eleq2d 2524 |
. 2
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7 | fvex 5897 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 3, 7 | eqeltri 2535 |
. . . . . . . 8
![]() ![]() ![]() ![]() |
9 | 8 | rabex 4567 |
. . . . . . 7
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10 | eleq1 2527 |
. . . . . . 7
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11 | 9, 10 | mpbiri 241 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 11 | adantl 472 |
. . . . 5
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13 | 12 | a1i 11 |
. . . 4
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14 | 13 | rexlimivv 2895 |
. . 3
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15 | eqeq1 2465 |
. . . . 5
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16 | 15 | anbi2d 715 |
. . . 4
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17 | 16 | 2rexbidv 2919 |
. . 3
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18 | 14, 17 | elab3 3203 |
. 2
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19 | 6, 18 | syl6bb 269 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-rep 4528 ax-sep 4538 ax-nul 4547 ax-pr 4652 ax-un 6609 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-reu 2755 df-rab 2757 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-iun 4293 df-br 4416 df-opab 4475 df-mpt 4476 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-ov 6317 df-lines 33110 |
This theorem is referenced by: islinei 33349 linepsubN 33361 isline2 33383 |
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