Theorem biimparc

Description: Importation inference from a logical equivalence. (Contributed by NM, 3-May-1994)

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

Proof

Step	Hyp	Ref	Expression
1		biimpa.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	biimprcd	$$⊢\chi \to \left(\phi \to \psi \right)$$
3	2	imp	$$⊢\left(\chi \wedge \phi \right)\to \psi$$