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Mirrors > Home > NFE Home > Th. List > ax10 | Unicode version |
Description: Derive set.mm's original ax-10 2140 from others. (Contributed by NM, 25-Jul-2015.) (Revised by NM, 7-Nov-2015.) |
Ref | Expression |
---|---|
ax10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax9v 1655 |
. 2
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2 | df-ex 1542 |
. . 3
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3 | dveeq2 1940 |
. . . . . . . 8
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4 | 3 | imp 418 |
. . . . . . 7
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5 | ax10lem6 1943 |
. . . . . . . 8
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6 | equcomi 1679 |
. . . . . . . . 9
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7 | 6 | alimi 1559 |
. . . . . . . 8
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8 | 5, 7 | syl6 29 |
. . . . . . 7
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9 | ax10lem5 1942 |
. . . . . . 7
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10 | 4, 8, 9 | syl56 30 |
. . . . . 6
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11 | 10 | exp3acom23 1372 |
. . . . 5
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12 | pm2.18 102 |
. . . . 5
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13 | 11, 12 | syl6 29 |
. . . 4
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14 | 13 | exlimdv 1636 |
. . 3
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15 | 2, 14 | syl5bir 209 |
. 2
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16 | 1, 15 | mpi 16 |
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: aecom 1946 ax10o 1952 axi10 2331 |
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