Theorem ibir

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004)

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

Proof

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