Theorem cadrot 1615

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

Assertion

Ref	Expression
cadrot	⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))

Proof of Theorem cadrot

Step	Hyp	Ref	Expression
1		cadcoma 1613	. 2 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜑, 𝜒))
2		cadcomb 1614	. 2 ⊢ (cadd(𝜓, 𝜑, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))
3	1, 2	bitri 277	1 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))

Syntax hints:   ↔ wb 208  caddwcad 1607

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 209  df-an 399  df-or 844  df-3or 1084  df-3an 1085  df-xor 1502  df-cad 1608

This theorem is referenced by: (None)