Theorem bibi1

Description: Theorem *4.86 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	bibi1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
2	1	bibi1d	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$