Theorem pm4.61 406

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 405	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓))
2	1	bicomi 223	1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∧ wa 397

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 206  df-an 398

This theorem is referenced by:  pm4.65  407  npss  4111  difin  4262  2nreu  4442  isf32lem2  10349  cat1  18047  nmo  31730  hashxpe  32019  bnj1253  34028  fphpd  41554  clsk1independent  42797  nabctnabc  45641  islindeps  47134