Theorem e2bi

Description: Biconditional form of e2 . syl6ib is e2bi without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2bi.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e2bi.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	e2bi	$$⊢\left(\phi ,\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e2bi.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e2bi.2	$$⊢\chi \leftrightarrow \theta$$
3	2	biimpi	$$⊢\chi \to \theta$$
4	1 3	e2	$$⊢\left(\phi ,\psi \to \theta \right)$$