Theorem pm4.61 441

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 440	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓))
2	1	bicomi 213	1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  pm4.65  442  npss  3679  difin  3823  isf32lem2  9059  nmo  28709  bnj1253  30339  unblimceq0  31668  fphpd  36398  rp-fakenanass  36879  clsk1independent  37364  nabctnabc  39747  islindeps  42036