Theorem pm2.38 716

Description: Theorem *2.38 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.)

Assertion

Ref	Expression
pm2.38	⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜒 ∨ 𝜑)))

Proof of Theorem pm2.38

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜒))
2	1	orim1d 701	1 ⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜒 ∨ 𝜑)))

Syntax hints:   → wi 4   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm2.36  717  pm2.37  718