Theorem orim2 965

Description: Axiom *1.6 (Sum) of [WhiteheadRussell] p. 97. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
orim2	⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

Proof of Theorem orim2

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜒))
2	1	orim2d 964	1 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 844

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845

This theorem is referenced by:  pm2.81  969  rb-ax1  1755  pthacycspth  33119