Theorem bitr2d

Description: Deduction form of bitr2i . (Contributed by NM, 9-Jun-2004)

	Ref	Expression
Hypotheses	bitr2d.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	bitr2d.2	$$⊢\phi \to \left(\chi \leftrightarrow \theta \right)$$
Assertion	bitr2d	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr2d.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		bitr2d.2	$$⊢\phi \to \left(\chi \leftrightarrow \theta \right)$$
3	1 2	bitrd	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$
4	3	bicomd	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$