Theorem wl-3xorbi2 37906

Description: Alternative form of wl-3xorbi 37905. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024.)

Assertion

Ref	Expression
wl-3xorbi2	⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ↔ 𝜓) ↔ 𝜒))

Proof of Theorem wl-3xorbi2

Step	Hyp	Ref	Expression
1		wl-3xorbi 37905	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒)))
2		biass 387	. 2 ⊢ (((𝜑 ↔ 𝜓) ↔ 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒)))
3	1, 2	bitr4i 280	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ↔ 𝜓) ↔ 𝜒))

Syntax hints:   ↔ wb 208  haddwhad 1603

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 857  df-ifp 1072  df-xor 1522  df-tru 1553  df-had 1604

This theorem is referenced by:  wl-3xorbi123d  37907  wl-3xorrot  37909  wl-3xorcoma  37910  wl-3xornot  37913