Theorem pm2.42

Description: Theorem *2.42 of WhiteheadRussell p. 106. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.42	⊢ ( ( ¬ 𝜑 ∨ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )
2		id	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜓 ) )
3	1 2	jaoi	⊢ ( ( ¬ 𝜑 ∨ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜓 ) )