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Mirrors > Home > MPE Home > Th. List > hadrot | Structured version Visualization version GIF version |
Description: Rotation law for the adder sum. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
hadrot | ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hadcoma 1590 | . 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒)) | |
2 | hadcomb 1592 | . 2 ⊢ (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑)) | |
3 | 1, 2 | bitri 276 | 1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 207 haddwhad 1584 |
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 208 df-xor 1496 df-had 1585 |
This theorem is referenced by: had1 1595 sadadd2lem2 15787 saddisjlem 15801 |
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