Theorem pm2.67-2 905

Description: Slight generalization of Theorem *2.67 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.67-2	⊢ (((𝜑 ∨ 𝜒) → 𝜓) → (𝜑 → 𝜓))

Proof of Theorem pm2.67-2

Step	Hyp	Ref	Expression
1		orc 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	imim1i 64	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) → (𝜑 → 𝜓))

This proof depends on syntax axioms:   → 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:  pm2.67  906  jaob  976  axprglem  5394