Theorem imbi2d

Description: Deduction adding an antecedent to both sides of a logical equivalence. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypothesis	imbid.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	imbi2d	$$⊢\phi \to \left(\left(\theta \to \psi \right)\leftrightarrow \left(\theta \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imbid.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	a1d	$$⊢\phi \to \left(\theta \to \left(\psi \leftrightarrow \chi \right)\right)$$
3	2	pm5.74d	$$⊢\phi \to \left(\left(\theta \to \psi \right)\leftrightarrow \left(\theta \to \chi \right)\right)$$