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Mirrors > Home > MPE Home > Th. List > hadnot | Structured version Unicode version |
Description: The half adder distributes over negation. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
hadnot |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xorneg 1363 |
. . . 4
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2 | biid 236 |
. . . 4
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3 | 1, 2 | xorbi12i 1364 |
. . 3
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4 | xorneg2 1362 |
. . 3
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5 | 3, 4 | bitr2i 250 |
. 2
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6 | df-had 1422 |
. . 3
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7 | 6 | notbii 296 |
. 2
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8 | df-had 1422 |
. 2
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9 | 5, 7, 8 | 3bitr4i 277 |
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-xor 1352 df-had 1422 |
This theorem is referenced by: had0 1446 |
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