Theorem biimpi

Description: Infer an implication from a logical equivalence. Inference associated with biimp . (Contributed by NM, 29-Dec-1992)

	Ref	Expression
Hypothesis	biimpi.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	biimpi	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		biimpi.1	$$⊢\phi \leftrightarrow \psi$$
2		biimp	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \to \psi \right)$$
3	1 2	ax-mp	$$⊢\phi \to \psi$$