Theorem pm4.64 387

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 385	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	bicomi 214	1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 196   ∨ wo 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 197  df-or 385

This theorem is referenced by:  pm4.66  436  ioran  511  dfifp3  1015  dfnf5  3952  fimaxg  8207  fiming  8404  kmlem8  8979  axgroth6  9650  dfconn2  21222  ifpimimb  37849  ifpor123g  37853  hirstL-ax3  41059