Theorem pm5.501

Description: Theorem *5.501 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.501	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \leftrightarrow \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.1im	$$⊢\phi \to \left(\psi \to \left(\phi \leftrightarrow \psi \right)\right)$$
2		biimp	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \to \psi \right)$$
3	2	com12	$$⊢\phi \to \left(\left(\phi \leftrightarrow \psi \right)\to \psi \right)$$
4	1 3	impbid	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \leftrightarrow \psi \right)\right)$$