Theorem wl-df3xor3 37902

Description: Alternative form of wl-df3xor2 37901. Copy of df-had 1604. (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 37901	. 2 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓 ⊻ 𝜒)))
2		xorass 1525	. 2 ⊢ (((𝜑 ⊻ 𝜓) ⊻ 𝜒) ↔ (𝜑 ⊻ (𝜓 ⊻ 𝜒)))
3	1, 2	bitr4i 280	1 ⊢ (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑 ⊻ 𝜓) ⊻ 𝜒))

Syntax hints:   ↔ wb 208   ⊻ wxo 1521  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: (None)