Theorem pm2.37 885

Description: Theorem *2.37 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.)

Assertion

Ref	Expression
pm2.37	⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜒)))

Proof of Theorem pm2.37

Step	Hyp	Ref	Expression
1		pm2.38 883	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜒 ∨ 𝜑)))
2		pm1.4 400	. 2 ⊢ ((𝜒 ∨ 𝜑) → (𝜑 ∨ 𝜒))
3	1, 2	syl6 34	1 ⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 382

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 196  df-or 384  df-an 385

This theorem is referenced by: (None)