Theorem bitr3

Description: Closed nested implication form of bitr3i . Derived automatically from bitr3VD . (Contributed by Alan Sare, 31-Dec-2011)

	Ref	Expression
Assertion	bitr3	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \leftrightarrow \chi \right)\to \left(\psi \leftrightarrow \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		bibi1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$
2	1	biimpd	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \leftrightarrow \chi \right)\to \left(\psi \leftrightarrow \chi \right)\right)$$