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Mirrors > Home > ILE Home > Th. List > ceqsalt | Unicode version |
Description: Closed theorem version of ceqsalg 2717. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsalt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2703 |
. . . 4
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2 | 1 | 3ad2ant3 1005 |
. . 3
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3 | bi1 117 |
. . . . . . 7
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4 | 3 | imim3i 61 |
. . . . . 6
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5 | 4 | al2imi 1435 |
. . . . 5
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6 | 5 | 3ad2ant2 1004 |
. . . 4
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7 | 19.23t 1656 |
. . . . 5
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8 | 7 | 3ad2ant1 1003 |
. . . 4
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9 | 6, 8 | sylibd 148 |
. . 3
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10 | 2, 9 | mpid 42 |
. 2
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11 | bi2 129 |
. . . . . . 7
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12 | 11 | imim2i 12 |
. . . . . 6
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13 | 12 | com23 78 |
. . . . 5
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14 | 13 | alimi 1432 |
. . . 4
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15 | 14 | 3ad2ant2 1004 |
. . 3
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16 | 19.21t 1562 |
. . . 4
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17 | 16 | 3ad2ant1 1003 |
. . 3
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18 | 15, 17 | mpbid 146 |
. 2
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19 | 10, 18 | impbid 128 |
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-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 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-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: ceqsralt 2716 |
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