Theorem pm4.64 845

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 844	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	bicomi 223	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∨ wo 843

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-or 844

This theorem is referenced by:  pm4.66  846  ioran  980  dfifp3  1062  fimaxg  8991  fiming  9187  kmlem8  9844  axgroth6  10515  dfconn2  22478  ifpimimb  41009  ifpor123g  41013  hirstL-ax3  44274