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Mirrors > Home > ILE Home > Th. List > unissb | Unicode version |
Description: Relationship involving membership, subset, and union. Exercise 5 of [Enderton] p. 26 and its converse. (Contributed by NM, 20-Sep-2003.) |
Ref | Expression |
---|---|
unissb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluni 3583 |
. . . . . 6
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2 | 1 | imbi1i 227 |
. . . . 5
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3 | 19.23v 1763 |
. . . . 5
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4 | 2, 3 | bitr4i 176 |
. . . 4
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5 | 4 | albii 1359 |
. . 3
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6 | alcom 1367 |
. . . 4
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7 | 19.21v 1753 |
. . . . . 6
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8 | impexp 250 |
. . . . . . . 8
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9 | bi2.04 237 |
. . . . . . . 8
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10 | 8, 9 | bitri 173 |
. . . . . . 7
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11 | 10 | albii 1359 |
. . . . . 6
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12 | dfss2 2934 |
. . . . . . 7
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13 | 12 | imbi2i 215 |
. . . . . 6
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14 | 7, 11, 13 | 3bitr4i 201 |
. . . . 5
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15 | 14 | albii 1359 |
. . . 4
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16 | 6, 15 | bitri 173 |
. . 3
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17 | 5, 16 | bitri 173 |
. 2
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18 | dfss2 2934 |
. 2
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19 | df-ral 2311 |
. 2
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20 | 17, 18, 19 | 3bitr4i 201 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-in 2924 df-ss 2931 df-uni 3581 |
This theorem is referenced by: uniss2 3611 ssunieq 3613 sspwuni 3739 pwssb 3740 bm2.5ii 4222 |
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