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Mirrors > Home > NFE Home > Th. List > had0 | Unicode version |
Description: If the first parameter is false, the half adder is equivalent to the XOR of the other two inputs. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
had0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | had1 1402 |
. . 3
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2 | hadnot 1393 |
. . 3
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3 | df-xor 1305 |
. . . . 5
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4 | xorneg 1313 |
. . . . 5
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5 | 3, 4 | bitr3i 242 |
. . . 4
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6 | 5 | con1bii 321 |
. . 3
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7 | 1, 2, 6 | 3bitr4g 279 |
. 2
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8 | 7 | con4bid 284 |
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-xor 1305 df-had 1380 |
This theorem is referenced by: (None) |
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