Theorem bitr3d

Description: Deduction form of bitr3i . (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	bitr3d.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	bitr3d.2	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	bitr3d	$$⊢\phi \to \left(\chi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr3d.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		bitr3d.2	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$
3	1	bicomd	$$⊢\phi \to \left(\chi \leftrightarrow \psi \right)$$
4	3 2	bitrd	$$⊢\phi \to \left(\chi \leftrightarrow \theta \right)$$