Theorem pm4.65 410

Description: Theorem *4.65 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.65	⊢ (¬ (¬ 𝜑 → 𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓))

Proof of Theorem pm4.65

Step	Hyp	Ref	Expression
1		pm4.61 409	1 ⊢ (¬ (¬ 𝜑 → 𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∧ wa 400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401

This theorem is used by:  ioran  999