Theorem neor

Description: Logical OR with an equality. (Contributed by NM, 29-Apr-2007)

	Ref	Expression
Assertion	neor	$$⊢\left(A=B\vee \psi \right)\leftrightarrow \left(A\ne B\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-or	$$⊢\left(A=B\vee \psi \right)\leftrightarrow \left(\neg A=B\to \psi \right)$$
2		df-ne	$$⊢A\ne B\leftrightarrow \neg A=B$$
3	2	imbi1i	$$⊢\left(A\ne B\to \psi \right)\leftrightarrow \left(\neg A=B\to \psi \right)$$
4	1 3	bitr4i	$$⊢\left(A=B\vee \psi \right)\leftrightarrow \left(A\ne B\to \psi \right)$$