Theorem bicom

Description: Commutative law for the biconditional. Theorem *4.21 of WhiteheadRussell p. 117. (Contributed by NM, 11-May-1993)

	Ref	Expression
Assertion	bicom	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\psi \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bicom1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \leftrightarrow \phi \right)$$
2		bicom1	$$⊢\left(\psi \leftrightarrow \phi \right)\to \left(\phi \leftrightarrow \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\psi \leftrightarrow \phi \right)$$