Metamath Proof Explorer

Theorem imnan

Description: Express an implication in terms of a negated conjunction. (Contributed by NM, 9-Apr-1994)

Ref Expression
Assertion imnan ( ( 𝜑 → ¬ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 df-an ⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 → ¬ 𝜓 ) )
2 1 con2bii ⊢ ( ( 𝜑 → ¬ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )