Theorem pm2.37

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

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

Proof

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