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Mirrors > Home > MPE Home > Th. List > cadan | Structured version Unicode version |
Description: Write the adder carry in conjunctive normal form. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof shortened by Wolf Lammen, 25-Sep-2018.) |
Ref | Expression |
---|---|
cadan |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3or 966 |
. . . 4
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2 | cador 1433 |
. . . 4
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3 | andi 862 |
. . . . 5
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4 | 3 | orbi1i 520 |
. . . 4
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5 | 1, 2, 4 | 3bitr4i 277 |
. . 3
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6 | ordir 860 |
. . 3
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7 | ordi 859 |
. . . 4
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8 | orcom 387 |
. . . . 5
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9 | simpl 457 |
. . . . . . 7
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10 | 9 | orcd 392 |
. . . . . 6
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11 | pm4.72 871 |
. . . . . 6
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12 | 10, 11 | mpbi 208 |
. . . . 5
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13 | 8, 12 | bitr4i 252 |
. . . 4
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14 | 7, 13 | anbi12i 697 |
. . 3
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15 | 5, 6, 14 | 3bitri 271 |
. 2
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16 | df-3an 967 |
. 2
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17 | 15, 16 | bitr4i 252 |
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 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-xor 1352 df-cad 1423 |
This theorem is referenced by: cadnot 1437 |
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