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Mirrors > Home > NFE Home > Th. List > cador | Unicode version |
Description: Write the adder carry in disjunctive normal form. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
cador |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cad 1381 |
. 2
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2 | xor2 1310 |
. . . . . . 7
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3 | 2 | rbaib 873 |
. . . . . 6
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4 | 3 | anbi1d 685 |
. . . . 5
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5 | ancom 437 |
. . . . 5
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6 | andir 838 |
. . . . 5
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7 | 4, 5, 6 | 3bitr3g 278 |
. . . 4
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8 | 7 | pm5.74i 236 |
. . 3
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9 | df-or 359 |
. . 3
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10 | 3orass 937 |
. . . 4
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11 | df-or 359 |
. . . 4
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12 | 10, 11 | bitri 240 |
. . 3
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13 | 8, 9, 12 | 3bitr4i 268 |
. 2
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14 | 1, 13 | bitri 240 |
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 177 df-or 359 df-an 360 df-3or 935 df-xor 1305 df-cad 1381 |
This theorem is referenced by: cadan 1392 cadnot 1394 cadcomb 1396 |
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