Theorem biort

Description: A disjunction with a true formula is equivalent to that true formula. (Contributed by NM, 23-May-1999)

	Ref	Expression
Assertion	biort	$$⊢\phi \to \left(\phi \leftrightarrow \left(\phi \vee \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\phi \to \phi$$
2		orc	$$⊢\phi \to \left(\phi \vee \psi \right)$$
3	1 2	2thd	$$⊢\phi \to \left(\phi \leftrightarrow \left(\phi \vee \psi \right)\right)$$