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Mirrors > Home > NFE Home > Th. List > 2exsb | Unicode version |
Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.) |
Ref | Expression |
---|---|
2exsb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsb 2130 |
. . . 4
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2 | 1 | exbii 1582 |
. . 3
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3 | excom 1741 |
. . 3
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4 | 2, 3 | bitri 240 |
. 2
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5 | exsb 2130 |
. . . . 5
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6 | impexp 433 |
. . . . . . . . 9
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7 | 6 | albii 1566 |
. . . . . . . 8
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8 | 19.21v 1890 |
. . . . . . . 8
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9 | 7, 8 | bitr2i 241 |
. . . . . . 7
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10 | 9 | albii 1566 |
. . . . . 6
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11 | 10 | exbii 1582 |
. . . . 5
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12 | 5, 11 | bitri 240 |
. . . 4
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13 | 12 | exbii 1582 |
. . 3
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14 | excom 1741 |
. . 3
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15 | 13, 14 | bitri 240 |
. 2
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16 | 4, 15 | bitri 240 |
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-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: 2eu6 2289 |
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