Theorem ee3bir

Description: Right-biconditional form of e3 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee3bir.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee3bir.2	$$⊢\tau \leftrightarrow \theta$$
Assertion	ee3bir	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee3bir.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee3bir.2	$$⊢\tau \leftrightarrow \theta$$
3	2	biimpri	$$⊢\theta \to \tau$$
4	1 3	syl8	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$