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Mirrors > Home > ILE Home > Th. List > ltordlem | Unicode version |
Description: Lemma for eqord1 8058. (Contributed by Mario Carneiro, 14-Jun-2014.) |
Ref | Expression |
---|---|
ltord.1 |
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ltord.2 |
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ltord.3 |
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ltord.4 |
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ltord.5 |
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ltord.6 |
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Ref | Expression |
---|---|
ltordlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltord.6 |
. . 3
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2 | 1 | ralrimivva 2467 |
. 2
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3 | breq1 3870 |
. . . 4
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4 | ltord.2 |
. . . . 5
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5 | 4 | breq1d 3877 |
. . . 4
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6 | 3, 5 | imbi12d 233 |
. . 3
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7 | breq2 3871 |
. . . 4
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8 | eqeq1 2101 |
. . . . . . 7
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9 | ltord.1 |
. . . . . . . 8
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10 | 9 | eqeq1d 2103 |
. . . . . . 7
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11 | 8, 10 | imbi12d 233 |
. . . . . 6
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12 | ltord.3 |
. . . . . 6
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13 | 11, 12 | chvarv 1867 |
. . . . 5
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14 | 13 | breq2d 3879 |
. . . 4
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15 | 7, 14 | imbi12d 233 |
. . 3
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16 | 6, 15 | rspc2v 2748 |
. 2
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17 | 2, 16 | mpan9 276 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-v 2635 df-un 3017 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 |
This theorem is referenced by: eqord1 8058 |
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