Theorem pm2.45 692

Description: Theorem *2.45 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.45	⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

Proof of Theorem pm2.45

Step	Hyp	Ref	Expression
1		orc 668	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	con3i 597	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-in1 579  ax-in2 580  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm2.47  694  ioran  704  dn1dc  906  eueq3dc  2789