Theorem pm4.64 863

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 862	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	bicomi 227	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  pm4.66  864  ioran  999  dfifp3  1081  fimaxg  9262  fiming  9476  kmlem8  10217  axgroth6  10894  dfconn2  23717  ifpimimb  44463  ifpor123g  44467  hirstL-ax3  47906