Theorem bicom1

Description: Commutative law for the biconditional. (Contributed by Wolf Lammen, 10-Nov-2012)

	Ref	Expression
Assertion	bicom1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biimpr	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \to \phi \right)$$
2		biimp	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\phi \to \psi \right)$$
3	1 2	impbid	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \leftrightarrow \phi \right)$$