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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 2560 |
. . . . 5
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3 | 1, 2 | syl 14 |
. . . 4
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4 | eueq 2706 |
. . . 4
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5 | 3, 4 | sylib 127 |
. . 3
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6 | eleq1 2097 |
. . . . . . 7
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7 | 1, 6 | syl5ibrcom 146 |
. . . . . 6
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8 | 7 | pm4.71rd 374 |
. . . . 5
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9 | reuhypd.2 |
. . . . . . 7
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10 | 9 | 3expa 1103 |
. . . . . 6
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11 | 10 | pm5.32da 425 |
. . . . 5
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12 | 8, 11 | bitr4d 180 |
. . . 4
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13 | 12 | eubidv 1905 |
. . 3
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14 | 5, 13 | mpbid 135 |
. 2
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15 | df-reu 2307 |
. 2
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16 | 14, 15 | sylibr 137 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-reu 2307 df-v 2553 |
This theorem is referenced by: reuhyp 4170 |
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