Theorem hadrot 1540

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

Assertion

Ref	Expression
hadrot	|- (hadd ( ph , ps , ch ) <-> hadd ( ps , ch , ph ) )

Proof of Theorem hadrot

Step	Hyp	Ref	Expression
1		hadcoma 1538	. 2 |- (hadd ( ph , ps , ch ) <-> hadd ( ps , ph , ch ) )
2		hadcomb 1539	. 2 |- (hadd ( ps , ph , ch ) <-> hadd ( ps , ch , ph ) )
3	1, 2	bitri 264	1 |- (hadd ( ph , ps , ch ) <-> hadd ( ps , ch , ph ) )

Syntax hints:   <-> wb 196  haddwhad 1532

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 197  df-xor 1465  df-had 1533

This theorem is referenced by:  had1  1542  sadadd2lem2  15172  saddisjlem  15186