Theorem wl-3xorrot 37412

Description: Rotation law for triple xor. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024.)

Assertion

Ref	Expression
wl-3xorrot	⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

Proof of Theorem wl-3xorrot

Step	Hyp	Ref	Expression
1		bicom 222	. 2 ⊢ ((𝜑 ↔ (𝜓 ↔ 𝜒)) ↔ ((𝜓 ↔ 𝜒) ↔ 𝜑))
2		wl-3xorbi 37408	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒)))
3		wl-3xorbi2 37409	. 2 ⊢ (hadd(𝜓, 𝜒, 𝜑) ↔ ((𝜓 ↔ 𝜒) ↔ 𝜑))
4	1, 2, 3	3bitr4i 303	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜒, 𝜑))

Syntax hints:   ↔ wb 206  haddwhad 1592

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 848  df-ifp 1063  df-xor 1511  df-tru 1542  df-had 1593

This theorem is referenced by:  wl-3xorcomb  37414