Theorem pm5.21

Description: Two propositions are equivalent if they are both false. Theorem *5.21 of WhiteheadRussell p. 124. (Contributed by NM, 21-May-1994)

	Ref	Expression
Assertion	pm5.21	⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.21im	⊢ ( ¬ 𝜑 → ( ¬ 𝜓 → ( 𝜑 ↔ 𝜓 ) ) )
2	1	imp	⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )