Theorem hadrot 1531

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 1529	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2		hadcomb 1530	. 2 ⊢ (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))
3	1, 2	bitri 263	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

Syntax hints:   ↔ wb 195  haddwhad 1523

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 196  df-xor 1457  df-had 1524

This theorem is referenced by:  had1  1533  sadadd2lem2  15010  saddisjlem  15024