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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > islshp | Structured version Visualization version Unicode version |
Description: The predicate "is a hyperplane" (of a left module or left vector space). (Contributed by NM, 29-Jun-2014.) |
Ref | Expression |
---|---|
lshpset.v |
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lshpset.n |
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lshpset.s |
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lshpset.h |
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Ref | Expression |
---|---|
islshp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lshpset.v |
. . . 4
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2 | lshpset.n |
. . . 4
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3 | lshpset.s |
. . . 4
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4 | lshpset.h |
. . . 4
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5 | 1, 2, 3, 4 | lshpset 32544 |
. . 3
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6 | 5 | eleq2d 2514 |
. 2
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7 | neeq1 2686 |
. . . . 5
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8 | uneq1 3581 |
. . . . . . . 8
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9 | 8 | fveq2d 5869 |
. . . . . . 7
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10 | 9 | eqeq1d 2453 |
. . . . . 6
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11 | 10 | rexbidv 2901 |
. . . . 5
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12 | 7, 11 | anbi12d 717 |
. . . 4
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13 | 12 | elrab 3196 |
. . 3
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14 | 3anass 989 |
. . 3
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15 | 13, 14 | bitr4i 256 |
. 2
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16 | 6, 15 | syl6bb 265 |
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-sep 4525 ax-nul 4534 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-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 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-iota 5546 df-fun 5584 df-fv 5590 df-lshyp 32543 |
This theorem is referenced by: islshpsm 32546 lshplss 32547 lshpne 32548 lshpnel2N 32551 lkrshp 32671 lshpset2N 32685 dochsatshp 35019 |
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