Theorem pm2.65

Description: Theorem *2.65 of WhiteheadRussell p. 107. Proof by contradiction. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 8-Mar-2013)

	Ref	Expression
Assertion	pm2.65	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → ¬ 𝜓 ) → ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		idd	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜑 → ¬ 𝜑 ) )
2		con3	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )
3	1 2	jad	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → ¬ 𝜓 ) → ¬ 𝜑 ) )