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	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.22	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜓 ∧ 𝜑 ) )
2		pm3.22	⊢ ( ( 𝜓 ∧ 𝜑 ) → ( 𝜑 ∧ 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) )