Theorem pm4.64 844

Description: Theorem *4.64 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.64	⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

Proof of Theorem pm4.64

Step	Hyp	Ref	Expression
1		df-or 843	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	bicomi 225	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 207   ∨ wo 842

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 208  df-or 843

This theorem is referenced by:  pm4.66  845  ioran  978  dfifp3  1058  fimaxg  8618  fiming  8815  kmlem8  9436  axgroth6  10103  dfconn2  21715  ifpimimb  39376  ifpor123g  39380  hirstL-ax3  42691