Theorem pm2.67-2 703

Description: Slight generalization of Theorem *2.67 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 9-Dec-2012.)

Assertion

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

Proof of Theorem pm2.67-2

Step	Hyp	Ref	Expression
1		orc 702	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	imim1i 60	1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) → (𝜑 → 𝜓))

Syntax hints:   → wi 4   ∨ wo 698

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  oibabs  704  pm2.67  733