Theorem e2bir

Description: Right biconditional form of e2 . syl6ibr is e2bir without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2bir.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e2bir.2	$$⊢\theta \leftrightarrow \chi$$
Assertion	e2bir	$$⊢\left(\phi ,\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e2bir.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e2bir.2	$$⊢\theta \leftrightarrow \chi$$
3	2	biimpri	$$⊢\chi \to \theta$$
4	1 3	e2	$$⊢\left(\phi ,\psi \to \theta \right)$$