Theorem pm2.45 728

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 702	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	con3i 622	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm2.47  730  ioran  742  dn1dc  950  eueq3dc  2900