Theorem ibd

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi . (Contributed by NM, 26-Jun-2004)

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

Proof

Step	Hyp	Ref	Expression
1		ibd.1	$$⊢\phi \to \left(\psi \to \left(\psi \leftrightarrow \chi \right)\right)$$
2		biimp	$$⊢\left(\psi \leftrightarrow \chi \right)\to \left(\psi \to \chi \right)$$
3	1 2	syli	$$⊢\phi \to \left(\psi \to \chi \right)$$