Theorem bitr

Description: Theorem *4.22 of WhiteheadRussell p. 117. bitri in closed form. (Contributed by NM, 3-Jan-2005)

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

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	biimpar	$$⊢\left(\left(\phi \leftrightarrow \psi \right)\wedge \left(\psi \leftrightarrow \chi \right)\right)\to \left(\phi \leftrightarrow \chi \right)$$