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Mirrors > Home > MPE Home > Th. List > nllyi | Structured version Visualization version Unicode version |
Description: The property of an
n-locally ![]() |
Ref | Expression |
---|---|
nllyi |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isnlly 20561 |
. . . 4
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2 | 1 | simprbi 471 |
. . 3
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3 | pweq 3945 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | ineq2d 3625 |
. . . . . 6
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5 | 4 | rexeqdv 2980 |
. . . . 5
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6 | 5 | raleqbi1dv 2981 |
. . . 4
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7 | 6 | rspccva 3135 |
. . 3
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8 | 2, 7 | sylan 479 |
. 2
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9 | elin 3608 |
. . . . . . 7
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10 | sneq 3969 |
. . . . . . . . . 10
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11 | 10 | fveq2d 5883 |
. . . . . . . . 9
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12 | 11 | eleq2d 2534 |
. . . . . . . 8
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13 | selpw 3949 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 13 | a1i 11 |
. . . . . . . 8
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15 | 12, 14 | anbi12d 725 |
. . . . . . 7
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16 | 9, 15 | syl5bb 265 |
. . . . . 6
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17 | 16 | anbi1d 719 |
. . . . 5
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18 | anass 661 |
. . . . 5
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19 | 17, 18 | syl6bb 269 |
. . . 4
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20 | 19 | rexbidv2 2888 |
. . 3
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21 | 20 | rspccva 3135 |
. 2
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22 | 8, 21 | stoic3 1668 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-iota 5553 df-fv 5597 df-ov 6311 df-nlly 20559 |
This theorem is referenced by: nlly2i 20568 llycmpkgen 20644 |
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