Theorem hadrot

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

	Ref	Expression
Assertion	hadrot	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜒 , 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		hadcoma	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜑 , 𝜒 ) )
2		hadcomb	⊢ ( hadd ( 𝜓 , 𝜑 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜒 , 𝜑 ) )
3	1 2	bitri	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜒 , 𝜑 ) )