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Mirrors > Home > ILE Home > Th. List > dvds2lem | Unicode version |
Description: A lemma to assist
theorems of ![]() |
Ref | Expression |
---|---|
dvds2lem.1 |
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dvds2lem.2 |
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dvds2lem.3 |
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dvds2lem.4 |
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dvds2lem.5 |
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Ref | Expression |
---|---|
dvds2lem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvds2lem.1 |
. . . . . 6
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2 | dvds2lem.2 |
. . . . . 6
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3 | divides 11343 |
. . . . . . 7
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4 | divides 11343 |
. . . . . . 7
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5 | 3, 4 | bi2anan9 578 |
. . . . . 6
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6 | 1, 2, 5 | syl2anc 406 |
. . . . 5
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7 | 6 | biimpd 143 |
. . . 4
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8 | reeanv 2574 |
. . . 4
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9 | 7, 8 | syl6ibr 161 |
. . 3
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10 | dvds2lem.4 |
. . . . 5
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11 | dvds2lem.5 |
. . . . 5
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12 | oveq1 5735 |
. . . . . . 7
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13 | 12 | eqeq1d 2123 |
. . . . . 6
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14 | 13 | rspcev 2760 |
. . . . 5
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15 | 10, 11, 14 | syl6an 1393 |
. . . 4
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16 | 15 | rexlimdvva 2531 |
. . 3
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17 | 9, 16 | syld 45 |
. 2
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18 | dvds2lem.3 |
. . 3
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19 | divides 11343 |
. . 3
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20 | 18, 19 | syl 14 |
. 2
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21 | 17, 20 | sylibrd 168 |
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 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-br 3896 df-opab 3950 df-iota 5046 df-fv 5089 df-ov 5731 df-dvds 11342 |
This theorem is referenced by: dvds2ln 11374 dvds2add 11375 dvds2sub 11376 dvdstr 11378 |
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