Theorem hadrot 1630

Description: Rotation law for the adder sum. (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 1628	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2		hadcomb 1629	. 2 ⊢ (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
3	1, 2	bitri 278	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

This proof depends on syntax axioms:   ↔ wb 209  haddwhad 1622

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-xor 1541  df-had 1623

This theorem is used by:  had1  1632  sadadd2lem2  16514  saddisjlem  16528