Theorem imbi2

Description: Theorem *4.85 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 19-May-2013)

	Ref	Expression
Assertion	imbi2	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\chi \to \phi \right)\leftrightarrow \left(\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
2	1	imbi2d	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\chi \to \phi \right)\leftrightarrow \left(\chi \to \psi \right)\right)$$