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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 2068 |
. . 3
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2 | eu2.1 |
. . . . . 6
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3 | 2 | nfri 1530 |
. . . . 5
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4 | 3 | eumo0 2069 |
. . . 4
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5 | 2 | mo23 2079 |
. . . 4
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6 | 4, 5 | syl 14 |
. . 3
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7 | 1, 6 | jca 306 |
. 2
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8 | 19.29r 1632 |
. . . 4
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9 | impexp 263 |
. . . . . . . . 9
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10 | 9 | albii 1481 |
. . . . . . . 8
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11 | 2 | 19.21 1594 |
. . . . . . . 8
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12 | 10, 11 | bitri 184 |
. . . . . . 7
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13 | 12 | anbi2i 457 |
. . . . . 6
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14 | abai 560 |
. . . . . 6
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15 | 13, 14 | bitr4i 187 |
. . . . 5
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16 | 15 | exbii 1616 |
. . . 4
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17 | 8, 16 | sylib 122 |
. . 3
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18 | 3 | eu1 2063 |
. . 3
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19 | 17, 18 | sylibr 134 |
. 2
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20 | 7, 19 | impbii 126 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-eu 2041 |
This theorem is referenced by: eu3h 2083 mo3h 2091 bm1.1 2174 reu2 2940 |
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