Theorem wl-3xorcomb 35629

Description: Commutative 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-3xorcomb	⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜑, 𝜒, 𝜓))

Proof of Theorem wl-3xorcomb

Step	Hyp	Ref	Expression
1		wl-3xorcoma 35628	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2		wl-3xorrot 35627	. 2 ⊢ (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜑, 𝜒, 𝜓))
3	1, 2	bitri 274	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜑, 𝜒, 𝜓))

Syntax hints:   ↔ wb 205  haddwhad 1597

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 206  df-an 396  df-or 844  df-ifp 1060  df-xor 1506  df-tru 1544  df-had 1598

This theorem is referenced by: (None)