Theorem e3bir

Description: Right biconditional form of e3 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3bir.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e3bir.2	$$⊢\tau \leftrightarrow \theta$$
Assertion	e3bir	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e3bir.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e3bir.2	$$⊢\tau \leftrightarrow \theta$$
3	2	biimpri	$$⊢\theta \to \tau$$
4	1 3	e3	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$