Theorem pm2.45 657

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 633	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	con3i 562	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm2.47  659  ioran  669  dn1dc  867  eueq3dc  2715