Theorem pm4.64 850

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 849	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	bicomi 224	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 206   ∨ wo 848

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-or 849

This theorem is referenced by:  pm4.66  851  ioran  986  dfifp3  1066  fimaxg  9323  fiming  9538  kmlem8  10198  axgroth6  10868  dfconn2  23427  ifpimimb  43517  ifpor123g  43521  hirstL-ax3  46904