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Mirrors > Home > NFE Home > Th. List > cadnot | Unicode version |
Description: The adder carry distributes over negation. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
cadnot |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ioran 950 |
. . 3
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2 | ianor 474 |
. . . 4
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3 | ianor 474 |
. . . 4
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4 | ianor 474 |
. . . 4
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5 | 2, 3, 4 | 3anbi123i 1140 |
. . 3
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6 | 1, 5 | bitri 240 |
. 2
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7 | cador 1391 |
. . 3
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8 | 7 | notbii 287 |
. 2
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9 | cadan 1392 |
. 2
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10 | 6, 8, 9 | 3bitr4i 268 |
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-3an 936 df-xor 1305 df-cad 1381 |
This theorem is referenced by: (None) |
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