Theorem pm4.61 408

Description: Theorem *4.61 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.61	⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem pm4.61

Step	Hyp	Ref	Expression
1		annim 407	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓))
2	1	bicomi 226	1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 208   ∧ wa 399

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 400

This theorem is referenced by:  pm4.65  409  npss  4067  difin  4224  2nreu  4398  isf32lem2  10311  cat1  18130  nmo  32689  hashxpe  33009  bnj1253  35312  fphpd  43393  clsk1independent  44622  nabctnabc  47525  islindeps  49075