Theorem biimpd

Description: Deduce an implication from a logical equivalence. Deduction associated with biimp and biimpi . (Contributed by NM, 11-Jan-1993)

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

Proof

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