Theorem pm4.63 402

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 401	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2	1	bicomi 227	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:  pm4.67  403  nqereu  10920  axacprim  36207  andnand1  36940