Theorem pm2.63

Description: Theorem *2.63 of WhiteheadRussell p. 107. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.63	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( ¬ 𝜑 ∨ 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.53	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) )
2		idd	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜓 → 𝜓 ) )
3	1 2	jaod	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( ¬ 𝜑 ∨ 𝜓 ) → 𝜓 ) )