Theorem pm4.63 400

Description: Theorem *4.63 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.63	⊢ (¬ (𝜑 → ¬ 𝜓) ↔ (𝜑 ∧ 𝜓))

Proof of Theorem pm4.63

Step	Hyp	Ref	Expression
1		df-an 399	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2	1	bicomi 226	1 ⊢ (¬ (𝜑 → ¬ 𝜓) ↔ (𝜑 ∧ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 208   ∧ wa 398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 399

This theorem is referenced by:  pm4.67  401  nqereu  10350  axacprim  32933  andnand1  33749