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Mirrors > Home > NFE Home > Th. List > 4exdistr | Unicode version |
Description: Distribution of existential quantifiers. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
4exdistr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 630 |
. . . . . . . 8
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2 | 1 | exbii 1582 |
. . . . . . 7
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3 | 19.42v 1905 |
. . . . . . . 8
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4 | 19.42v 1905 |
. . . . . . . . 9
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5 | 4 | anbi2i 675 |
. . . . . . . 8
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6 | 19.42v 1905 |
. . . . . . . . . 10
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7 | 6 | anbi2i 675 |
. . . . . . . . 9
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8 | 7 | anbi2i 675 |
. . . . . . . 8
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9 | 3, 5, 8 | 3bitri 262 |
. . . . . . 7
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10 | 2, 9 | bitri 240 |
. . . . . 6
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11 | 10 | exbii 1582 |
. . . . 5
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12 | 19.42v 1905 |
. . . . 5
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13 | 19.42v 1905 |
. . . . . 6
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14 | 13 | anbi2i 675 |
. . . . 5
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15 | 11, 12, 14 | 3bitri 262 |
. . . 4
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16 | 15 | exbii 1582 |
. . 3
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17 | 19.42v 1905 |
. . 3
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18 | 16, 17 | bitri 240 |
. 2
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19 | 18 | exbii 1582 |
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-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 |
This theorem is referenced by: (None) |
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