Theorem orcom

Description: Commutative law for disjunction. Theorem *4.31 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 15-Nov-2012)

	Ref	Expression
Assertion	orcom	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( 𝜓 ∨ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm1.4	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜓 ∨ 𝜑 ) )
2		pm1.4	⊢ ( ( 𝜓 ∨ 𝜑 ) → ( 𝜑 ∨ 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( 𝜓 ∨ 𝜑 ) )