Theorem 3impexpbicomi

Description: Inference associated with 3impexpbicom . Derived automatically from 3impexpbicomiVD . (Contributed by Alan Sare, 31-Dec-2011)

	Ref	Expression
Hypothesis	3impexpbicomi.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \leftrightarrow \tau \right)$$
Assertion	3impexpbicomi	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\tau \leftrightarrow \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3impexpbicomi.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \leftrightarrow \tau \right)$$
2	1	bicomd	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\tau \leftrightarrow \theta \right)$$
3	2	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\tau \leftrightarrow \theta \right)\right)\right)$$