Theorem xorcomOLD

Description: Obsolete version of xorcom as of 21-Apr-2024. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	xorcomOLD	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \left(\psi ⊻\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bicom	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\psi \leftrightarrow \phi \right)$$
2	1	notbii	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\psi \leftrightarrow \phi \right)$$
3		df-xor	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$
4		df-xor	$$⊢\left(\psi ⊻\phi \right)\leftrightarrow \neg \left(\psi \leftrightarrow \phi \right)$$
5	2 3 4	3bitr4i	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \left(\psi ⊻\phi \right)$$