Theorem orim2 983

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 23	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜒))
2	1	orim2d 982	1 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

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-an 402  df-or 862

This theorem is used by:  pm2.81  987  rb-ax1  1785  pthacycspth  35688