Theorem cadrot 1614

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 1612	. 2 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜑, 𝜒))
2		cadcomb 1613	. 2 ⊢ (cadd(𝜓, 𝜑, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))
3	1, 2	bitri 275	1 ⊢ (cadd(𝜑, 𝜓, 𝜒) ↔ cadd(𝜓, 𝜒, 𝜑))

Syntax hints:   ↔ wb 206  caddwcad 1606

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 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-xor 1512  df-cad 1607

This theorem is referenced by:  wl-df-3mintru2  37485