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Mirrors > Home > ILE Home > Th. List > mopick2 | Unicode version |
Description: "At most one" can show the existence of a common value. In this case we can infer existence of conjunction from a conjunction of existence, and it is one way to achieve the converse of 19.40 1611. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
mopick2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbmo1 2038 |
. . . 4
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2 | hbe1 1472 |
. . . 4
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3 | 1, 2 | hban 1527 |
. . 3
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4 | mopick 2078 |
. . . . . 6
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5 | 4 | ancld 323 |
. . . . 5
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6 | 5 | anim1d 334 |
. . . 4
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7 | df-3an 965 |
. . . 4
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8 | 6, 7 | syl6ibr 161 |
. . 3
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9 | 3, 8 | eximdh 1591 |
. 2
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10 | 9 | 3impia 1179 |
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-3an 965 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 |
This theorem is referenced by: (None) |
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