Theorem imbi2i

Description: Introduce an antecedent to both sides of a logical equivalence. This and the next three rules are useful for building up wff's around a definition, in order to make use of the definition. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 6-Feb-2013)

	Ref	Expression
Hypothesis	imbi2i.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	imbi2i	$$⊢\left(\chi \to \phi \right)\leftrightarrow \left(\chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imbi2i.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢\chi \to \left(\phi \leftrightarrow \psi \right)$$
3	2	pm5.74i	$$⊢\left(\chi \to \phi \right)\leftrightarrow \left(\chi \to \psi \right)$$