Theorem wl-df3xor3 38211

Description: Alternative form of wl-df3xor2 38210. Copy of df-had 1624. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 1-May-2024.)

Assertion

Ref	Expression
wl-df3xor3	⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ⊻ 𝜓) ⊻ 𝜒))

Proof of Theorem wl-df3xor3

Step	Hyp	Ref	Expression
1		wl-df3xor2 38210	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓 ⊻ 𝜒)))
2		xorass 1545	. 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   ⊻ wxo 1541  haddwhad 1623

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 402  df-or 862  df-ifp 1079  df-xor 1542  df-tru 1573  df-had 1624

This theorem is used by: (None)