Theorem wl-3xorbi2

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

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

Proof

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