Theorem wl-hadcomb 34772

Description: Commutative law for the adders sum. (Contributed by Mario Carneiro, 4-Sep-2016.) Alternative definition. (Revised by Wolf Lammen, 24-Apr-2024.)

Assertion

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

Proof of Theorem wl-hadcomb

Step	Hyp	Ref	Expression
1		wl-hadcoma 34771	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜓, 𝜑, 𝜒))
2		wl-hadrot 34770	. 2 ⊢ (hadd(𝜓, 𝜑, 𝜒) ↔ hadd(𝜑, 𝜒, 𝜓))
3	1, 2	bitri 277	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ hadd(𝜑, 𝜒, 𝜓))

Syntax hints:   ↔ wb 208  haddwhad 1593

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-ifp 1058  df-xor 1502  df-tru 1540  df-had 1594

This theorem is referenced by: (None)