Theorem ibi

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 17-Oct-2003)

	Ref	Expression
Hypothesis	ibi.1	$$⊢\phi \to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ibi	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		ibi.1	$$⊢\phi \to \left(\phi \leftrightarrow \psi \right)$$
2		id	$$⊢\phi \to \phi$$
3	2 1	mpbid	$$⊢\phi \to \psi$$