Theorem bi2imp

Description: Importation inference similar to imp , except both implications of the hypothesis are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi2imp.1	$$⊢\phi \leftrightarrow \left(\psi \leftrightarrow \chi \right)$$
Assertion	bi2imp	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		bi2imp.1	$$⊢\phi \leftrightarrow \left(\psi \leftrightarrow \chi \right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
3	2	biimpa	$$⊢\left(\phi \wedge \psi \right)\to \chi$$