Theorem hadrot

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

	Ref	Expression
Assertion	hadrot	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow hadd\left(\psi ,\chi ,\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		hadcoma	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow hadd\left(\psi ,\phi ,\chi \right)$$
2		hadcomb	$$⊢hadd\left(\psi ,\phi ,\chi \right)\leftrightarrow hadd\left(\psi ,\chi ,\phi \right)$$
3	1 2	bitri	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow hadd\left(\psi ,\chi ,\phi \right)$$