Theorem pm4.57

Description: Theorem *4.57 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.57	⊢ ( ¬ ( ¬ 𝜑 ∧ ¬ 𝜓 ) ↔ ( 𝜑 ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		oran	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∧ ¬ 𝜓 ) )
2	1	bicomi	⊢ ( ¬ ( ¬ 𝜑 ∧ ¬ 𝜓 ) ↔ ( 𝜑 ∨ 𝜓 ) )