Theorem pm2.45 895

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 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	con3i 155	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ 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:  pm2.47  897  dn1  1073  eueq3  3676  outpasch  29088  acopyeu  29196  tgasa1  29230  unbdqndv2lem1  37155