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Mirrors > Home > ILE Home > Th. List > eu2 | Unicode version |
Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.) |
Ref | Expression |
---|---|
eu2.1 |
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Ref | Expression |
---|---|
eu2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 1930 |
. . 3
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2 | eu2.1 |
. . . . . 6
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3 | 2 | nfri 1412 |
. . . . 5
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4 | 3 | eumo0 1931 |
. . . 4
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5 | 2 | mo23 1941 |
. . . 4
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6 | 4, 5 | syl 14 |
. . 3
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7 | 1, 6 | jca 290 |
. 2
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8 | 19.29r 1512 |
. . . 4
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9 | impexp 250 |
. . . . . . . . 9
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10 | 9 | albii 1359 |
. . . . . . . 8
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11 | 2 | 19.21 1475 |
. . . . . . . 8
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12 | 10, 11 | bitri 173 |
. . . . . . 7
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13 | 12 | anbi2i 430 |
. . . . . 6
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14 | abai 494 |
. . . . . 6
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15 | 13, 14 | bitr4i 176 |
. . . . 5
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16 | 15 | exbii 1496 |
. . . 4
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17 | 8, 16 | sylib 127 |
. . 3
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18 | 3 | eu1 1925 |
. . 3
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19 | 17, 18 | sylibr 137 |
. 2
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20 | 7, 19 | impbii 117 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 |
This theorem is referenced by: eu3h 1945 mo3h 1953 bm1.1 2025 reu2 2729 |
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