Theorem pm2.01d

Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993) (Proof shortened by Wolf Lammen, 5-Mar-2013)

	Ref	Expression
Hypothesis	pm2.01d.1	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) )
Assertion	pm2.01d	⊢ ( 𝜑 → ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		pm2.01d.1	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) )
2		id	⊢ ( ¬ 𝜓 → ¬ 𝜓 )
3	1 2	pm2.61d1	⊢ ( 𝜑 → ¬ 𝜓 )