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Mirrors > Home > MPE Home > Th. List > cadrot | Structured version Visualization version GIF version |
Description: Rotation law for the adder carry. (Contributed by Mario Carneiro, 4-Sep-2016.) |
Ref | Expression |
---|---|
cadrot | ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cadcoma 1542 | . 2 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜑, 𝜒)) | |
2 | cadcomb 1543 | . 2 ⊢ (cadd(𝜓, 𝜑, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑)) | |
3 | 1, 2 | bitri 263 | 1 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 caddwcad 1536 |
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 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 df-xor 1457 df-cad 1537 |
This theorem is referenced by: (None) |
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