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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 3837 |
. . 3
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2 | neeq1 2268 |
. . . . 5
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3 | nfcv 2228 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
4 | nfcv 2228 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
5 | disji.1 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 3, 4, 5 | csbhypf 2966 |
. . . . . . 7
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7 | 6 | ineq1d 3200 |
. . . . . 6
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8 | 7 | eqeq1d 2096 |
. . . . 5
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9 | 2, 8 | imbi12d 232 |
. . . 4
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10 | neeq2 2269 |
. . . . 5
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11 | nfcv 2228 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
12 | nfcv 2228 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
13 | disji.2 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 11, 12, 13 | csbhypf 2966 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 14 | ineq2d 3201 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | eqeq1d 2096 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 10, 16 | imbi12d 232 |
. . . 4
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18 | 9, 17 | rspc2v 2734 |
. . 3
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19 | 1, 18 | mpan9 275 |
. 2
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20 | 19 | 3impia 1140 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-rex 2365 df-reu 2366 df-rmo 2367 df-v 2621 df-sbc 2841 df-csb 2934 df-dif 3001 df-in 3005 df-nul 3287 df-disj 3823 |
This theorem is referenced by: (None) |
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