Theorem pm4.65r 682

Description: One direction of Theorem *4.65 of [WhiteheadRussell] p. 120. The converse holds in classical logic. (Contributed by Jim Kingdon, 28-Jul-2018.)

Assertion

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

Proof of Theorem pm4.65r

Step	Hyp	Ref	Expression
1		annimim 681	1 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) → ¬ (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-in1 609  ax-in2 610

This theorem is referenced by: (None)