Theorem e3bi

Description: Biconditional form of e3 . syl8ib is e3bi without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3bi.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e3bi.2	$$⊢\theta \leftrightarrow \tau$$
Assertion	e3bi	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e3bi.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e3bi.2	$$⊢\theta \leftrightarrow \tau$$
3	2	biimpi	$$⊢\theta \to \tau$$
4	1 3	e3	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$