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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > lsatlspsn | Structured version Visualization version Unicode version |
Description: The span of a non-zero singleton is an atom. (Contributed by NM, 16-Jan-2015.) |
Ref | Expression |
---|---|
lsatset.v |
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lsatset.n |
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lsatset.z |
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lsatset.a |
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lsatlspsn.w |
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lsatlspsn.x |
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Ref | Expression |
---|---|
lsatlspsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lsatlspsn.x |
. . 3
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2 | eqid 2450 |
. . 3
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3 | sneq 3977 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | fveq2d 5867 |
. . . . 5
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5 | 4 | eqeq2d 2460 |
. . . 4
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6 | 5 | rspcev 3149 |
. . 3
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7 | 1, 2, 6 | sylancl 667 |
. 2
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8 | lsatlspsn.w |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | lsatset.v |
. . . 4
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10 | lsatset.n |
. . . 4
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11 | lsatset.z |
. . . 4
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12 | lsatset.a |
. . . 4
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13 | 9, 10, 11, 12 | islsat 32551 |
. . 3
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14 | 8, 13 | syl 17 |
. 2
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15 | 7, 14 | mpbird 236 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 ax-un 6580 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-mpt 4462 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-fv 5589 df-lsatoms 32536 |
This theorem is referenced by: lsatspn0 32560 dvh4dimlem 35005 dochsnshp 35015 lclkrlem2a 35069 lclkrlem2c 35071 lclkrlem2e 35073 lcfrlem20 35124 mapdrvallem2 35207 mapdpglem20 35253 mapdpglem30a 35257 mapdpglem30b 35258 hdmaprnlem3eN 35423 hdmaprnlem16N 35427 |
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