Theorem wl-3xorbi2 38148

Description: Alternative form of wl-3xorbi 38147. (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 38147	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒)))
2		biass 388	. 2 ⊢ (((𝜑 ↔ 𝜓) ↔ 𝜒) ↔ (𝜑 ↔ (𝜓 ↔ 𝜒)))
3	1, 2	bitr4i 281	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ↔ 𝜓) ↔ 𝜒))

This proof depends on syntax axioms:   ↔ wb 209  haddwhad 1622

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ifp 1078  df-xor 1541  df-tru 1572  df-had 1623

This theorem is used by:  wl-3xorbi123d  38149  wl-3xorrot  38151  wl-3xorcoma  38152  wl-3xornot  38155