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Mirrors > Home > MPE Home > Th. List > disjor | Structured version Visualization version Unicode version |
Description: Two ways to say that a
collection ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
disjor.1 |
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Ref | Expression |
---|---|
disjor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-disj 4346 |
. 2
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2 | ralcom4 3034 |
. . 3
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3 | orcom 393 |
. . . . . . 7
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4 | df-or 376 |
. . . . . . 7
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5 | neq0 3710 |
. . . . . . . . . 10
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6 | elin 3585 |
. . . . . . . . . . 11
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7 | 6 | exbii 1722 |
. . . . . . . . . 10
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8 | 5, 7 | bitri 257 |
. . . . . . . . 9
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9 | 8 | imbi1i 331 |
. . . . . . . 8
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10 | 19.23v 1822 |
. . . . . . . 8
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11 | 9, 10 | bitr4i 260 |
. . . . . . 7
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12 | 3, 4, 11 | 3bitri 279 |
. . . . . 6
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13 | 12 | ralbii 2804 |
. . . . 5
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14 | ralcom4 3034 |
. . . . 5
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15 | 13, 14 | bitri 257 |
. . . 4
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16 | 15 | ralbii 2804 |
. . 3
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17 | disjor.1 |
. . . . . 6
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18 | 17 | eleq2d 2515 |
. . . . 5
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19 | 18 | rmo4 3199 |
. . . 4
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20 | 19 | albii 1695 |
. . 3
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21 | 2, 16, 20 | 3bitr4i 285 |
. 2
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22 | 1, 21 | bitr4i 260 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rmo 2745 df-v 3015 df-dif 3375 df-in 3379 df-nul 3700 df-disj 4346 |
This theorem is referenced by: disjors 4360 disjxiun 4371 disjxun 4372 otsndisj 4679 otiunsndisj 4680 qsdisj2 7428 cshwsdisj 15080 dyadmbl 22570 2spotdisj 25801 2spotiundisj 25802 2spotmdisj 25808 numclwwlkdisj 25820 disjnf 28191 disjorsf 28200 poimirlem26 31968 mblfinlem2 31980 ndisj2 37384 nnfoctbdjlem 38354 iundjiun 38359 otiunsndisjX 39098 |
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