Theorem pm4.56

Description: Theorem *4.56 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.56	⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ∨ 𝜓 ) )

Proof

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