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Mirrors > Home > HSE Home > Th. List > dmdi | Structured version Visualization version Unicode version |
Description: Consequence of the dual modular pair property. (Contributed by NM, 27-Apr-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dmdi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmdbr 27964 |
. . . . 5
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2 | 1 | biimpd 212 |
. . . 4
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3 | sseq2 3422 |
. . . . . 6
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4 | ineq1 3595 |
. . . . . . . 8
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5 | 4 | oveq1d 6291 |
. . . . . . 7
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6 | ineq1 3595 |
. . . . . . 7
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7 | 5, 6 | eqeq12d 2467 |
. . . . . 6
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8 | 3, 7 | imbi12d 326 |
. . . . 5
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9 | 8 | rspcv 3114 |
. . . 4
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10 | 2, 9 | sylan9 667 |
. . 3
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11 | 10 | 3impa 1205 |
. 2
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12 | 11 | imp32 439 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-sn 3937 df-pr 3939 df-op 3943 df-uni 4169 df-br 4375 df-opab 4434 df-iota 5525 df-fv 5569 df-ov 6279 df-dmd 27946 |
This theorem is referenced by: dmdi2 27969 dmdsl3 27980 csmdsymi 27999 mdsymlem1 28068 |
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