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Mirrors > Home > NFE 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 2227 |
. . 3
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2 | eu2.1 |
. . . . 5
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3 | 2 | eumo0 2228 |
. . . 4
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4 | 2 | mo 2226 |
. . . 4
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5 | 3, 4 | sylib 188 |
. . 3
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6 | 1, 5 | jca 518 |
. 2
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7 | 19.29r 1597 |
. . . 4
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8 | impexp 433 |
. . . . . . . . 9
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9 | 8 | albii 1566 |
. . . . . . . 8
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10 | 2 | 19.21 1796 |
. . . . . . . 8
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11 | 9, 10 | bitri 240 |
. . . . . . 7
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12 | 11 | anbi2i 675 |
. . . . . 6
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13 | abai 770 |
. . . . . 6
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14 | 12, 13 | bitr4i 243 |
. . . . 5
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15 | 14 | exbii 1582 |
. . . 4
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16 | 7, 15 | sylib 188 |
. . 3
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17 | 2 | eu1 2225 |
. . 3
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18 | 16, 17 | sylibr 203 |
. 2
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19 | 6, 18 | impbii 180 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 |
This theorem is referenced by: eu3 2230 bm1.1 2338 reu2 3025 |
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