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Mirrors > Home > MPE Home > Th. List > hadnot | Structured version Visualization version Unicode version |
Description: The adder sum distributes over negation. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof shortened by Wolf Lammen, 11-Jul-2020.) |
Ref | Expression |
---|---|
hadnot | hadd hadd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notbi 309 | . . 3 | |
2 | 1 | bibi1i 328 | . 2 |
3 | xor3 372 | . . 3 | |
4 | hadbi 1537 | . . 3 hadd | |
5 | 3, 4 | xchnxbir 323 | . 2 hadd |
6 | hadbi 1537 | . 2 hadd | |
7 | 2, 5, 6 | 3bitr4i 292 | 1 hadd hadd |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 haddwhad 1532 |
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 197 df-xor 1465 df-had 1533 |
This theorem is referenced by: had0 1543 |
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