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

Proof

Step	Hyp	Ref	Expression
1		wl-df3xor2	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\phi ⊻\left(\psi ⊻\chi \right)\right)$$
2		xorass	$$⊢\left(\left(\phi ⊻\psi \right)⊻\chi \right)\leftrightarrow \left(\phi ⊻\left(\psi ⊻\chi \right)\right)$$
3	1 2	bitr4i	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\left(\phi ⊻\psi \right)⊻\chi \right)$$