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Mirrors > Home > ILE Home > Th. List > disji2 | Unicode version |
Description: Property of a disjoint
collection: if ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
disji.1 |
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disji.2 |
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Ref | Expression |
---|---|
disji2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disjnims 3929 |
. . 3
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2 | neeq1 2322 |
. . . . 5
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3 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
4 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
5 | disji.1 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 3, 4, 5 | csbhypf 3043 |
. . . . . . 7
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7 | 6 | ineq1d 3281 |
. . . . . 6
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8 | 7 | eqeq1d 2149 |
. . . . 5
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9 | 2, 8 | imbi12d 233 |
. . . 4
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10 | neeq2 2323 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
12 | nfcv 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
13 | disji.2 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 11, 12, 13 | csbhypf 3043 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 14 | ineq2d 3282 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | eqeq1d 2149 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 10, 16 | imbi12d 233 |
. . . 4
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18 | 9, 17 | rspc2v 2806 |
. . 3
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19 | 1, 18 | mpan9 279 |
. 2
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20 | 19 | 3impia 1179 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-reu 2424 df-rmo 2425 df-v 2691 df-sbc 2914 df-csb 3008 df-dif 3078 df-in 3082 df-nul 3369 df-disj 3915 |
This theorem is referenced by: (None) |
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