Theorem e1bi

Description: Biconditional form of e1a . sylib is e1bi without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1bi.1	$$⊢\left(\phi \to \psi \right)$$
	e1bi.2	$$⊢\psi \leftrightarrow \chi$$
Assertion	e1bi	$$⊢\left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		e1bi.1	$$⊢\left(\phi \to \psi \right)$$
2		e1bi.2	$$⊢\psi \leftrightarrow \chi$$
3	2	biimpi	$$⊢\psi \to \chi$$
4	1 3	e1a	$$⊢\left(\phi \to \chi \right)$$