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	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\left(\phi \leftrightarrow \psi \right)\leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-3xorbi	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\phi \leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$
2		biass	$$⊢\left(\left(\phi \leftrightarrow \psi \right)\leftrightarrow \chi \right)\leftrightarrow \left(\phi \leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$
3	1 2	bitr4i	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\left(\phi \leftrightarrow \psi \right)\leftrightarrow \chi \right)$$