Theorem cadrot 1397

Description: Rotation law for 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 1395	. 2 ⊢ (cadd(φ, ψ, χ) ↔ cadd(ψ, φ, χ))
2		cadcomb 1396	. 2 ⊢ (cadd(ψ, φ, χ) ↔ cadd(ψ, χ, φ))
3	1, 2	bitri 240	1 ⊢ (cadd(φ, ψ, χ) ↔ cadd(ψ, χ, φ))

Syntax hints:   ↔ wb 176  caddwcad 1379

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 177  df-or 359  df-an 360  df-3or 935  df-xor 1305  df-cad 1381

This theorem is referenced by: (None)