Theorem hadrot 1390

Description: Rotation law for triple XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

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

Proof of Theorem hadrot

Step	Hyp	Ref	Expression
1		hadcoma 1388	. 2 ⊢ (hadd(φ, ψ, χ) ↔ hadd(ψ, φ, χ))
2		hadcomb 1389	. 2 ⊢ (hadd(ψ, φ, χ) ↔ hadd(ψ, χ, φ))
3	1, 2	bitri 240	1 ⊢ (hadd(φ, ψ, χ) ↔ hadd(ψ, χ, φ))

Syntax hints:   ↔ wb 176  haddwhad 1378

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 177  df-xor 1305  df-had 1380

This theorem is referenced by: (None)