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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 11798 |
. . . . . . 7
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4 | divides 11798 |
. . . . . . 7
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5 | 3, 4 | bi2anan9 606 |
. . . . . 6
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6 | 1, 2, 5 | syl2anc 411 |
. . . . 5
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7 | 6 | biimpd 144 |
. . . 4
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8 | reeanv 2647 |
. . . 4
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9 | 7, 8 | imbitrrdi 162 |
. . 3
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10 | dvds2lem.4 |
. . . . 5
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11 | dvds2lem.5 |
. . . . 5
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12 | oveq1 5884 |
. . . . . . 7
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13 | 12 | eqeq1d 2186 |
. . . . . 6
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14 | 13 | rspcev 2843 |
. . . . 5
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15 | 10, 11, 14 | syl6an 1434 |
. . . 4
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16 | 15 | rexlimdvva 2602 |
. . 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 11798 |
. . 3
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20 | 18, 19 | syl 14 |
. 2
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21 | 17, 20 | sylibrd 169 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-iota 5180 df-fv 5226 df-ov 5880 df-dvds 11797 |
This theorem is referenced by: dvds2ln 11833 dvds2add 11834 dvds2sub 11835 dvdstr 11837 |
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