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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > pcl0bN | Structured version Visualization version Unicode version |
Description: The projective subspace closure of the empty subspace. (Contributed by NM, 13-Sep-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pcl0b.a |
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pcl0b.c |
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Ref | Expression |
---|---|
pcl0bN |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pcl0b.a |
. . . . 5
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2 | pcl0b.c |
. . . . 5
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3 | 1, 2 | pclssidN 33460 |
. . . 4
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4 | eqimss 3484 |
. . . 4
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5 | 3, 4 | sylan9ss 3445 |
. . 3
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6 | ss0 3765 |
. . 3
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7 | 5, 6 | syl 17 |
. 2
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8 | fveq2 5865 |
. . . 4
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9 | 2 | pcl0N 33487 |
. . . 4
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10 | 8, 9 | sylan9eqr 2507 |
. . 3
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11 | 10 | adantlr 721 |
. 2
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12 | 7, 11 | impbida 843 |
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 ax-un 6583 ax-riotaBAD 32525 |
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-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rmo 2745 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-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-riota 6252 df-ov 6293 df-oprab 6294 df-undef 7020 df-preset 16173 df-poset 16191 df-plt 16204 df-lub 16220 df-glb 16221 df-join 16222 df-meet 16223 df-p0 16285 df-p1 16286 df-lat 16292 df-clat 16354 df-oposet 32742 df-ol 32744 df-oml 32745 df-covers 32832 df-ats 32833 df-atl 32864 df-cvlat 32888 df-hlat 32917 df-psubsp 33068 df-pmap 33069 df-pclN 33453 df-polarityN 33468 |
This theorem is referenced by: pclfinclN 33515 |
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