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Mirrors > Home > ILE Home > Th. List > reuhypd | Unicode version |
Description: A theorem useful for eliminating restricted existential uniqueness hypotheses. (Contributed by NM, 16-Jan-2012.) |
Ref | Expression |
---|---|
reuhypd.1 |
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reuhypd.2 |
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Ref | Expression |
---|---|
reuhypd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reuhypd.1 |
. . . . 5
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2 | elex 2700 |
. . . . 5
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3 | 1, 2 | syl 14 |
. . . 4
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4 | eueq 2859 |
. . . 4
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5 | 3, 4 | sylib 121 |
. . 3
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6 | eleq1 2203 |
. . . . . . 7
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7 | 1, 6 | syl5ibrcom 156 |
. . . . . 6
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8 | 7 | pm4.71rd 392 |
. . . . 5
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9 | reuhypd.2 |
. . . . . . 7
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10 | 9 | 3expa 1182 |
. . . . . 6
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11 | 10 | pm5.32da 448 |
. . . . 5
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12 | 8, 11 | bitr4d 190 |
. . . 4
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13 | 12 | eubidv 2008 |
. . 3
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14 | 5, 13 | mpbid 146 |
. 2
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15 | df-reu 2424 |
. 2
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16 | 14, 15 | sylibr 133 |
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 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-reu 2424 df-v 2691 |
This theorem is referenced by: reuhyp 4401 |
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