Theorem pm4.61 404

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 403	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓))
2	1	bicomi 224	1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 206   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  pm4.65  405  npss  4123  difin  4278  2nreu  4450  isf32lem2  10392  cat1  18151  nmo  32518  hashxpe  32817  bnj1253  35010  fphpd  42804  clsk1independent  44036  nabctnabc  46881  islindeps  48299