Theorem ibib

Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994) (Proof shortened by Wolf Lammen, 24-Jan-2013)

	Ref	Expression
Assertion	ibib	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \left(\phi \leftrightarrow \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.501	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \leftrightarrow \psi \right)\right)$$
2	1	pm5.74i	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \left(\phi \leftrightarrow \psi \right)\right)$$