Theorem wl-df3xor3

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

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

Proof

Step	Hyp	Ref	Expression
1		wl-df3xor2	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( 𝜑 ⊻ ( 𝜓 ⊻ 𝜒 ) ) )
2		xorass	⊢ ( ( ( 𝜑 ⊻ 𝜓 ) ⊻ 𝜒 ) ↔ ( 𝜑 ⊻ ( 𝜓 ⊻ 𝜒 ) ) )
3	1 2	bitr4i	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( ( 𝜑 ⊻ 𝜓 ) ⊻ 𝜒 ) )