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Mirrors > Home > ILE Home > Th. List > ltordlem | Unicode version |
Description: Lemma for eqord1 8454. (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 2569 |
. 2
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3 | breq1 4018 |
. . . 4
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4 | ltord.2 |
. . . . 5
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5 | 4 | breq1d 4025 |
. . . 4
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6 | 3, 5 | imbi12d 234 |
. . 3
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7 | breq2 4019 |
. . . 4
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8 | eqeq1 2194 |
. . . . . . 7
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9 | ltord.1 |
. . . . . . . 8
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10 | 9 | eqeq1d 2196 |
. . . . . . 7
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11 | 8, 10 | imbi12d 234 |
. . . . . 6
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12 | ltord.3 |
. . . . . 6
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13 | 11, 12 | chvarv 1947 |
. . . . 5
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14 | 13 | breq2d 4027 |
. . . 4
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15 | 7, 14 | imbi12d 234 |
. . 3
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16 | 6, 15 | rspc2v 2866 |
. 2
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17 | 2, 16 | mpan9 281 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-v 2751 df-un 3145 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 |
This theorem is referenced by: eqord1 8454 |
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