Theorem cadrot

Description: Rotation law for the adder carry. (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Assertion	cadrot	$$⊢cadd\left(\phi ,\psi ,\chi \right)\leftrightarrow cadd\left(\psi ,\chi ,\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		cadcoma	$$⊢cadd\left(\phi ,\psi ,\chi \right)\leftrightarrow cadd\left(\psi ,\phi ,\chi \right)$$
2		cadcomb	$$⊢cadd\left(\psi ,\phi ,\chi \right)\leftrightarrow cadd\left(\psi ,\chi ,\phi \right)$$
3	1 2	bitri	$$⊢cadd\left(\phi ,\psi ,\chi \right)\leftrightarrow cadd\left(\psi ,\chi ,\phi \right)$$