Theorem ancom

Description: Commutative law for conjunction. Theorem *4.3 of WhiteheadRussell p. 118. (Contributed by NM, 25-Jun-1998) (Proof shortened by Wolf Lammen, 4-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		pm3.22	$$⊢\left(\phi \wedge \psi \right)\to \left(\psi \wedge \phi \right)$$
2		pm3.22	$$⊢\left(\psi \wedge \phi \right)\to \left(\phi \wedge \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\psi \wedge \phi \right)$$