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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 2022 |
. 2
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2 | excom 1625 |
. . . 4
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3 | hbe1 1454 |
. . . . . 6
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4 | 3 | hbmo 2014 |
. . . . 5
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5 | 19.8a 1552 |
. . . . . . 7
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6 | 5 | moimi 2040 |
. . . . . 6
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7 | df-mo 1979 |
. . . . . 6
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8 | 6, 7 | sylib 121 |
. . . . 5
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9 | 4, 8 | eximdh 1573 |
. . . 4
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10 | 2, 9 | syl5bi 151 |
. . 3
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11 | 10 | impcom 124 |
. 2
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12 | 1, 11 | sylbi 120 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 |
This theorem is referenced by: (None) |
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