Theorem pm2.36 966

Description: Theorem *2.36 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.)

Assertion

Ref	Expression
pm2.36	⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜒 ∨ 𝜑)))

Proof of Theorem pm2.36

Step	Hyp	Ref	Expression
1		pm1.4 865	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))
2		pm2.38 965	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜒 ∨ 𝜑)))
3	1, 2	syl5 34	1 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜒 ∨ 𝜑)))

Syntax hints:   → wi 4   ∨ wo 843

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 396  df-or 844

This theorem is referenced by: (None)