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Mirrors > Home > ILE Home > Th. List > 2euex | Unicode version |
Description: Double quantification with existential uniqueness. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
2euex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eu5 2083 |
. 2
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2 | excom 1674 |
. . . 4
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3 | hbe1 1505 |
. . . . . 6
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4 | 3 | hbmo 2075 |
. . . . 5
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5 | 19.8a 1600 |
. . . . . . 7
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6 | 5 | moimi 2101 |
. . . . . 6
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7 | df-mo 2040 |
. . . . . 6
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8 | 6, 7 | sylib 122 |
. . . . 5
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9 | 4, 8 | eximdh 1621 |
. . . 4
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10 | 2, 9 | biimtrid 152 |
. . 3
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11 | 10 | impcom 125 |
. 2
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12 | 1, 11 | sylbi 121 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 |
This theorem is referenced by: (None) |
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