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Mirrors > Home > ILE Home > Th. List > moanim | Unicode version |
Description: Introduction of a conjunct into at-most-one quantifier. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
moanim.1 |
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Ref | Expression |
---|---|
moanim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anandi 580 |
. . . . 5
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2 | 1 | imbi1i 237 |
. . . 4
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3 | impexp 261 |
. . . 4
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4 | sban 1929 |
. . . . . . 7
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5 | moanim.1 |
. . . . . . . . 9
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6 | 5 | sbf 1751 |
. . . . . . . 8
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7 | 6 | anbi1i 454 |
. . . . . . 7
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8 | 4, 7 | bitr2i 184 |
. . . . . 6
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9 | 8 | anbi2i 453 |
. . . . 5
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10 | 9 | imbi1i 237 |
. . . 4
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11 | 2, 3, 10 | 3bitr3i 209 |
. . 3
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12 | 11 | 2albii 1448 |
. 2
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13 | 5 | 19.21 1563 |
. . 3
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14 | 19.21v 1846 |
. . . 4
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15 | 14 | albii 1447 |
. . 3
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16 | ax-17 1507 |
. . . . 5
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17 | 16 | mo3h 2053 |
. . . 4
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18 | 17 | imbi2i 225 |
. . 3
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19 | 13, 15, 18 | 3bitr4ri 212 |
. 2
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20 | ax-17 1507 |
. . 3
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21 | 20 | mo3h 2053 |
. 2
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22 | 12, 19, 21 | 3bitr4ri 212 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 |
This theorem is referenced by: moanimv 2075 moaneu 2076 moanmo 2077 |
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